previous :: next
Open Problems on Syzygies and Hilbert Functions
I. Peeva and M. Stillman
Source: J. Commut. Algebra Volume 1, Number 1
(2009), 159-195.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jca/1229376154
Digital Object Identifier: doi:10.1216/JCA-2009-1-1-159
Mathematical Reviews number (MathSciNet): MR2462384
Zentralblatt MATH identifier: 05673526
References
D. Anick, Counterexample to a conjecture of Serre, Ann. Math., 115 (1982), 1-33.
Mathematical Reviews (MathSciNet): MR644015
Digital Object Identifier: doi:10.2307/1971338
A. Aramova, L. L. Avramov, J. Herzog, Resolutions of monomial ideals and cohomology over exterior algebras, Trans. Amer. Math. Soc., 352 (2000), 579-594.
Mathematical Reviews (MathSciNet): MR1603874
Zentralblatt MATH: 0930.13011
Digital Object Identifier: doi:10.1090/S0002-9947-99-02298-9
JSTOR: links.jstor.org
L. L. Avramov, Infinite free resolutions, in Six lectures on commutative algebra (Bellaterra, 1996), Progr. Math., 166, Birkh�user, Basel, (1998), 1-118.
Mathematical Reviews (MathSciNet): MR1648664
--------, Local algebra and rational homotopy, Astérisque, 113-114 (1984), 15-43.
Mathematical Reviews (MathSciNet): MR749041
--------, Homological asymptotics of modules over local rings, in Commutative Algebra, M. Hochster, C. Huneke and J. Sally, Editors, Math. Sci. Res. Inst. Publ. 15 Springer, New York, (1989), 33-62.
Mathematical Reviews (MathSciNet): MR1015512
Zentralblatt MATH: 0788.18010
--------, Problems on infinite free resolutions, Free Resolutions in Commutative Algebra and Algebraic Geometry, D. Eisenbud and C. Huneke, Editors, Jones and Bartlett Publishers, Boston, London, (1992), 3-23.
Mathematical Reviews (MathSciNet): MR1165314
Zentralblatt MATH: 0778.13010
L. L. Avramov, R.-O. Buchweitz, Lower bounds for Betti numbers, Compositio Math., 86, (1993), 147-158.
Mathematical Reviews (MathSciNet): MR1214454
--------, Homological algebra modulo a regular sequence with special attention to codimension two, J. Algebra, 230 (2000), 24-67.
Mathematical Reviews (MathSciNet): MR1774757
Zentralblatt MATH: 1011.13007
Digital Object Identifier: doi:10.1006/jabr.1999.7953
L. L. Avramov, D. Eisenbud, Regularity of modules over a Koszul algebra, J. Algebra, 153 (1992), 85-90.
Mathematical Reviews (MathSciNet): MR1195407
Zentralblatt MATH: 0770.13006
Digital Object Identifier: doi:10.1016/0021-8693(92)90149-G
L. Avramov, D. Grayson, Resolutions and cohomology over complete intersections, in Computations in algebraic geometry with Macaulay 2, Algorithms Comput. Math. 8 Springer, Berlin, (2002), 131-178.
Mathematical Reviews (MathSciNet): MR1949551
Zentralblatt MATH: 0994.13006
L. L. Avramov, S. Iyengar, and L. Sega, Free resolutions over short local rings, preprint.
Mathematical Reviews (MathSciNet): MR2439635
Zentralblatt MATH: 1153.13011
Digital Object Identifier: doi:10.1112/jlms/jdn027
L. L. Avramov, I. Peeva, Finite regularity and Koszul algebras, American J. Math., 123 (2001), 275-281.
Mathematical Reviews (MathSciNet): MR1828224
Zentralblatt MATH: 1053.13500
Digital Object Identifier: doi:10.1353/ajm.2001.0008
L. L. Avramov, Li-Chuan Sun, Cohomology operators defined by a deformation, J. Algebra, 204 (1998), 684-710.
Mathematical Reviews (MathSciNet): MR1624432
Zentralblatt MATH: 0915.13009
Digital Object Identifier: doi:10.1006/jabr.1997.7317
D. Bayer and D. Mumford, What can be computed in algebraic geometry? in Computational Algebraic Geometry and Commutative Algebra, D. Eisenbud and L. Robbiano (eds.), Cambridge Univ. Press, Cambridge, (1993), 1-48.
Mathematical Reviews (MathSciNet): MR1253986
Zentralblatt MATH: 0846.13017
D. Bayer and M. Stillman, MACAULAY\thinspace--\thinspacea system for computation, algebraic geometry and commutative algebra, (1997), available from www.math.columbia.edu/$\tilde\ $bayer/Macaulay.
--------, On the complexity of computing syzygies, J. Symbolic Comput., 6 (1988), 135--147.
Mathematical Reviews (MathSciNet): MR988409
Zentralblatt MATH: 0667.68053
Digital Object Identifier: doi:10.1016/S0747-7171(88)80039-7
A. Berglund: Poincarè, series of monomial rings, J. Algebra, 295 (2006), 211-230.
Mathematical Reviews (MathSciNet): MR2188858
Digital Object Identifier: doi:10.1016/j.jalgebra.2005.04.008
A. Bertram, L. Ein, R. Lazarsfeld, Vanishing theorems, a theorem of Severi, and the equations defining projective varieties, J. Amer. Math. Soc., 4 (1991), 587--602.
Mathematical Reviews (MathSciNet): MR1092845
Zentralblatt MATH: 0762.14012
Digital Object Identifier: doi:10.2307/2939270
JSTOR: links.jstor.org
M. Boij, J. Söderberg, Graded Betti numbers of Cohen-Macaulay modules and the Multiplicity conjecture, J. London Math. Soc., to appear.
Mathematical Reviews (MathSciNet): MR2427053
Zentralblatt MATH: 05309689
Digital Object Identifier: doi:10.1112/jlms/jdn013
--------, Betti numbers of graded modules and the Multiplicity Conjecture in the non-Cohen-Macaulay case, preprint.
W. Bruns, J. Gubeladze, and N.Trung, Problems and algorithms for affine semigroups, Semigroup Forum, 64 (2002), 180-212.
Mathematical Reviews (MathSciNet): MR1876854
Zentralblatt MATH: 1018.20048
W. Bruns, T. Römer, $h$-vectors of Gorenstein polytopes, J. Combin. Theory Ser. A, 114 (2007), 65-76.
Mathematical Reviews (MathSciNet): MR2275581
Zentralblatt MATH: 1108.52013
Digital Object Identifier: doi:10.1016/j.jcta.2006.03.003
G. Caviglia, The pinched Veronese is Koszul, preprint.
Mathematical Reviews (MathSciNet): MR2563140
Digital Object Identifier: doi:10.1007/s10801-009-0176-1
H. Charalambous and G. Evans, Problems on Betti numbers of finite length modules, Free resolutions in commutative algebra and algebraic geometry (Sundance, UT, 1990), Res. Notes Math. 2, Jones and Bartlett, Boston, (1992), 25-33.
Mathematical Reviews (MathSciNet): MR1165315
Zentralblatt MATH: 0767.13005
M. Chardin, Regularity, in Syzygies and Hilbert functions, I. Peeva editor, Lect. Notes Pure Appl. Math., 254 (2007), CRC Press.
Mathematical Reviews (MathSciNet): MR2309924
M. Chardin and C. D'Cruz, Castelnuovo-Mumford regularity: examples of curves and surfaces, J. ALgebra, 270 (2003), 347-360.
Mathematical Reviews (MathSciNet): MR2016666
Zentralblatt MATH: 1056.14065
Digital Object Identifier: doi:10.1016/S0021-8693(03)00493-9
M. Chardin, V. Gasharov, and I. Peeva, Maximal Betti numbers, Proc. Amer. Math. Soc., 130 (2002), 1877--1880.
Mathematical Reviews (MathSciNet): MR1896017
Zentralblatt MATH: 0987.13004
Digital Object Identifier: doi:10.1090/S0002-9939-02-06471-7
JSTOR: links.jstor.org
M. Chardin and B. Ulrich, Liaison and Castelnuovo-Mumford regularity, Amer. J. Math., 124 (2002), 1103-1124.
Mathematical Reviews (MathSciNet): MR1939782
Zentralblatt MATH: 1029.14016
Digital Object Identifier: doi:10.1353/ajm.2002.0035
G. Clements and B. Lindström, A generalization of a combinatorial theorem of Macaulay, J. Combinatorial Theory, 7 (1969), 230-238.
Mathematical Reviews (MathSciNet): MR246781
Digital Object Identifier: doi:10.1016/S0021-9800(69)80016-5
A. Conca, Gröbner basis for spaces of quadrics of low codimension, Adv. Appl. Math., 24 (2000), 111-124.
Mathematical Reviews (MathSciNet): MR1748965
Digital Object Identifier: doi:10.1006/aama.1999.0676
A. Conca and J. Herzog, Castelnuovo-Mumford regularity of products of ideals, Collect. Math., 54 (2003), 137-152.
Mathematical Reviews (MathSciNet): MR1995137
H. Derksen and J. Sidman, A sharp bound for the Castelnuovo-Mumford regularity of subspace arrangements, Adv. Math., 172 (2002), 151-157.
Mathematical Reviews (MathSciNet): MR1942401
Zentralblatt MATH: 1040.13009
Digital Object Identifier: doi:10.1016/S0001-8708(02)00019-1
C. Dodd, A. Marks, V. Meyerson, Victor, and B. Richert, Minimal Betti numbers, Comm. Algebra, 35 (2007), 759--772.
Mathematical Reviews (MathSciNet): MR2305230
Zentralblatt MATH: 1122.13002
Digital Object Identifier: doi:10.1080/00927870601115617
J. Eagon and V. Reiner, Resolutions of Stanley-Reisner rings and Alexander duality, J. Pure Appl. Algebra, 130 (1998), 265-275.
Mathematical Reviews (MathSciNet): MR1633767
Zentralblatt MATH: 0941.13016
Digital Object Identifier: doi:10.1016/S0022-4049(97)00097-2
D. Eisenbud, Free resolutions, commutative algebra and algebraic geometry, (Sundance, UT, 1990), Res. Notes Math. 2, Jones and Bartlett, Boston, MA, (1992), 51-78.
Mathematical Reviews (MathSciNet): MR1165318
Zentralblatt MATH: 0792.14015
--------, Green's conjecture: an orientation for algebraists, Free resolutions in commutative algebra and algebraic geometry (Sundance, UT, 1990), Res. Notes Math. 2, Jones and Bartlett, Boston, MA, (1992), 51-78.
Zentralblatt MATH: 0792.14015
--------, Homological algebra on a complete intersection with an application to group representations, Trans. Amer. Math. Soc., 260 (1980), 35-64.
Mathematical Reviews (MathSciNet): MR570778
Digital Object Identifier: doi:10.2307/1999875
JSTOR: links.jstor.org
--------, Lectures on the geometry of syzygies, Trends in commutative algebra, Cambridge Univ. Press, Cambridge, Math. Sci. Res. Inst. Publ., 51 (2004), 115-152.
Mathematical Reviews (MathSciNet): MR2132650
Zentralblatt MATH: 1115.13019
--------, The geometry of syzygies. A second course in commutative algebra and algebraic geometry, Graduate Texts in Mathematics, 229 Springer-Verlag, New York, (2005).
Mathematical Reviews (MathSciNet): MR2103875
--------, An exterior view of modules and sheaves, Advances in algebra and geometry, (Hyderabad, 2001), Hindustan Book Agency, New Delhi, (2003), 209--216.
Mathematical Reviews (MathSciNet): MR1988957
Zentralblatt MATH: 1031.14006
--------, Periodic resolutions over exterior algebras, Special issue in celebration of Claudio Procesi's 60th birthday, J. Algebra, 258 (2002), 348-361.
Mathematical Reviews (MathSciNet): MR1958910
Zentralblatt MATH: 1081.13005
Digital Object Identifier: doi:10.1016/S0021-8693(02)00511-2
D. Eisenbud, G. Floystad, and F.-O. Schreyer, Sheaf cohomology and free resolutions over exterior algebras, Trans. Amer. Math. Soc., 355 (2003), 4397-4426.
Mathematical Reviews (MathSciNet): MR1990756
Zentralblatt MATH: 1063.14021
Digital Object Identifier: doi:10.1090/S0002-9947-03-03291-4
JSTOR: links.jstor.org
D. Eisenbud, G. Floystad, and J. Weyman, The existence of pure free resolutions, preprint.
D. Eisenbud and S. Goto, Linear free resolutions and minimal multiplicity, J. Algebra, 88 (1984), 89-133.
Mathematical Reviews (MathSciNet): MR741934
Zentralblatt MATH: 0531.13015
Digital Object Identifier: doi:10.1016/0021-8693(84)90092-9
D. Eisenbud, M. Green, and J. Harris, Higher Castelnuovo Theory, Astérisque, 218 (1993), 187-202.
Mathematical Reviews (MathSciNet): MR1265314
Zentralblatt MATH: 0819.14001
D. Eisenbud, M. Green, K. Hulek and S. Popescu, Restricting linear syzygies: algebra and geometry, Compositio Math., 141 (2005), 1460-1478.
Mathematical Reviews (MathSciNet): MR2188445
Zentralblatt MATH: 1086.14044
Digital Object Identifier: doi:10.1112/S0010437X05001776
D. Eisenbud and C. Huneke, A finiteness property of infinite resolutions, J. Pure Appl. Algebra, 201 (2005), 284-294. \vfill
Mathematical Reviews (MathSciNet): MR2158760
Zentralblatt MATH: 1091.13012
Digital Object Identifier: doi:10.1016/j.jpaa.2004.12.048
D. Eisenbud, C. Huneke, and B. Ulrich, The regularity of Tor and graded Betti numbers, Amer. J. Math., 128 (2006), 573-605.
Mathematical Reviews (MathSciNet): MR2230917
Zentralblatt MATH: 1105.13017
Digital Object Identifier: doi:10.1353/ajm.2006.0022
D. Eisenbud, I. Peeva, Standard decomposition in generic coordinates, preprint.
D. Eisenbud, A. Reeves, and B. Totaro, Initial ideals, Veronese subrings, and rates of algebras, Adv. Math., 109 (1994), 168-187.
Mathematical Reviews (MathSciNet): MR1304751
Zentralblatt MATH: 0839.13013
Digital Object Identifier: doi:10.1006/aima.1994.1085
D. Eisenbud and F-O. Schreyer, Betti numbers of graded modules and cohomology of vector bundles, preprint.
Mathematical Reviews (MathSciNet): MR2505303
Digital Object Identifier: doi:10.1090/S0894-0347-08-00620-6
M. Falk, and R. Randell, On the homotopy theory of arrangements. II, Arrangements---Tokyo 1998, Adv. Stud. Pure Math., 27 Kinokuniya, Tokyo, (2000), 93-125.
Mathematical Reviews (MathSciNet): MR1796895
Zentralblatt MATH: 0990.32006
C. Francisco and B. Richert, Lex-plus-powers ideals, Syzygies and Hilbert functions, I. Peeva editor, Lect. Notes Pure Appl. Math., 254 (2007), CRC Press.
Mathematical Reviews (MathSciNet): MR2309928
Zentralblatt MATH: 1125.13008
R. Fröberg, An inequality for Hilbert series of graded algebras, Math. Scand., 46 (1985), 117-144.
Mathematical Reviews (MathSciNet): MR813632
Zentralblatt MATH: 0582.13007
V. Gasharov, N. Horwitz, and I. Peeva, Hilbert functions over toric rings, special volume of the Michigan Math. J., dedicated to Mel Hochster.
Mathematical Reviews (MathSciNet): MR2492457
Zentralblatt MATH: 05604536
Digital Object Identifier: doi:10.1307/mmj/1220879413
Project Euclid: euclid.mmj/1220879413
V. Gasharov and I. Peeva, Boundedness versus periodicity, Trans. Amer. Math. Soc., 320 (1990), 569--580.
Mathematical Reviews (MathSciNet): MR967311
Zentralblatt MATH: 0706.13020
Digital Object Identifier: doi:10.2307/2001689
JSTOR: links.jstor.org
V. Gasharov, I. Peeva, and V. Welker, Coordinate subspace arrangements and monomial ideals, Proceedings of the Osaka meeting on Computational Commutative Algebra and Combinatorics, Advanced Studies in Pure Mathematics, 33 (2002), 65-74.
Mathematical Reviews (MathSciNet): MR1890096
Zentralblatt MATH: 1068.14064
A. Geramita, T. Harima, and Y. Shin, Extremal point sets and Gorenstein ideals, Adv. Math., 152 (2000), 78--119.
Mathematical Reviews (MathSciNet): MR1762121
Zentralblatt MATH: 0965.13011
Digital Object Identifier: doi:10.1006/aima.1998.1889
A. V. Geramita, P. Maroscia and L. Roberts, The Hilbert Function of a Reduced $k$-Algebra, J. London Math. Soc., 28 (1983), 443-452.
Mathematical Reviews (MathSciNet): MR724713
Zentralblatt MATH: 0535.13012
Digital Object Identifier: doi:10.1112/jlms/s2-28.3.443
A. Geramita, J. Migliore, and L. Sabourin, On the first infinitesimal neighborhood of a linear configuration of points in $ \bf P^ 2$, J. Algebra, 298 (2006), 563-611.
Mathematical Reviews (MathSciNet): MR2217628
Zentralblatt MATH: 1107.14048
Digital Object Identifier: doi:10.1016/j.jalgebra.2006.01.035
A. Geramita, and F. Orecchia, Minimally generating ideals defining certain tangent cones, J. Algebra, 78 (1982), 36-57.
Mathematical Reviews (MathSciNet): MR677711
Zentralblatt MATH: 0502.14001
Digital Object Identifier: doi:10.1016/0021-8693(82)90101-6
D. Grayson and M. Stillman, MACAULAY 2\thinspace--\thinspacea system for computation in algebraic geometry and commutative algebra, (1997), available from http://www.math.uiuc.edu/Macaulay2/.
M. Green, Generic initial ideals, Six lectures on commutative algebra, Birkhäuser, Progress in Mathematics 166 (1998), 119-185.
Mathematical Reviews (MathSciNet): MR1648665
G-M. Greuel, G. Pfister, and H. Sch�nemann, SINGULAR\thinspace--\thinspacea system for computation in algebraic geometry and commutative algebra, (1997), available from http://www.singular.uni-kl.de/.
L. Gruson, R. Lazarsfeld and C. Peskine, On a theorem of Castelnuovo, and the equations defining space curves, Inventiones mathematicae, 72 (1983), 491-506.
Mathematical Reviews (MathSciNet): MR704401
Zentralblatt MATH: 0565.14014
Digital Object Identifier: doi:10.1007/BF01398398
E. Guardo, A. Van Tuyl, The minimal resolutions of double points in $\bf P^ 1\times\bf P^1$ with ACM support, J. Pure Appl. Algebra, 211 (2007), 784-800. \vfill
Mathematical Reviews (MathSciNet): MR2344229
Zentralblatt MATH: 1126.13013
Digital Object Identifier: doi:10.1016/j.jpaa.2007.04.005
H. Ha, Multigraded regularity, $a^*$-,invariant and the minimal free resolution, J. Algebra, 310 (2007), 156--179.
Mathematical Reviews (MathSciNet): MR2307787
Zentralblatt MATH: 1142.13010
Digital Object Identifier: doi:10.1016/j.jalgebra.2006.12.016
B. Harbourne, Problems and progress: a survey on fat points in $\bf P^ 2$. Zero-dimensional schemes and applications (Naples, 2000), Queen's Papers in Pure and Appl. Math., Queen's Univ., Kingston, ON, 123 (2002), 85--132.
Mathematical Reviews (MathSciNet): MR1898832
Zentralblatt MATH: 1052.14052
R. Hartshorne, Connectedness of the Hilbert scheme, Publ. Math. IHES, 29 (1966), 5-48.
Mathematical Reviews (MathSciNet): MR213368
M. Hering, H. Schenck, and G. Smith, Syzygies, multigraded regularity and toric varieties, Compos. Math., 142 (2006), 1499-1506.
Mathematical Reviews (MathSciNet): MR2278757
Zentralblatt MATH: 1111.14052
Digital Object Identifier: doi:10.1112/S0010437X0600251X
J. Herzog, Finite free resolutions, Computational commutative and non-commutative algebraic geometry, NATO Sci. Ser. III Comput. Syst. Sci., IOS, Amsterdam, 196 (2005), 118-144.
Mathematical Reviews (MathSciNet): MR2179195
Zentralblatt MATH: 1105.13012
--------, Generic initial ideals and graded Betti numbers, Computational commutative algebra and combinatorics (Osaka, 1999), Adv. Stud. Pure Math, Math. Soc. Japan, Tokyo, 33 (2002), 75-120.
Mathematical Reviews (MathSciNet): MR1890097
Zentralblatt MATH: 1034.13009
J. Herzog, A. Jahan, and S. Yassemi, Stanley decompositions and partitionable simplicial complexes, J. Algebraic Combin., 27 (2008), 113-125.
Mathematical Reviews (MathSciNet): MR2366164
Digital Object Identifier: doi:10.1007/s10801-007-0076-1
T. Hibi and S. Murai, The behaviour of Betti numbers via algebraic shifting and combinatorial shifting, preprint.
T. Hibi, H. Nishida, and H. Ohsugi, Hilbert functions of squarefree Veronese subrings, Proceedings of the 4th Symposium on Algebra, Languages and Computation, (Osaka, 2000), Osaka Prefect. Univ., Sakai, (2001), 65-70.
Mathematical Reviews (MathSciNet): MR1845867
Zentralblatt MATH: 1096.13521
D. Hilbert, Über the Theorie von algebraischen Formen, Math. Ann. 36 (1890), 473-534. An English translation is available in Hilbert's Invariant Theory Papers, Math. Sci. Press, (1978).
Mathematical Reviews (MathSciNet): MR1510634
Digital Object Identifier: doi:10.1007/BF01208503
--------, Über die vollen Invariantensysteme, Math. Ann. 42 (1893), 313-373. An English translation is available in Hilbert's Invariant Theory Papers, Math. Sci. Press, (1978).
Mathematical Reviews (MathSciNet): MR1510781
Digital Object Identifier: doi:10.1007/BF01444162
F. Hirzebruch, Arrangements of lines and algebraic surfaces, Arithmetic and Geometry, vol. II, Progress in Math., 36, Birkhäuser, Boston, (1983), pp. 113-140.
Mathematical Reviews (MathSciNet): MR717609
Zentralblatt MATH: 0527.14033
A. Jahan, Stanley decompositions of squarefree modules and Alexander duality, preprint.
M. Jöllenbeck, V. Welker, Resolution of the residue field via algebraic discrete Morse theory, Memoirs of the AMS, to appear.
G. Kaempf, and T. Römer, Homological properties of Orlik-Solomon algebras, preprint.
G. Katona, A theorem for finite sets, Theory of Graphs, (P. Erdös and G. Katona, eds.), Academic Press, New York (1968), 187-207.
Mathematical Reviews (MathSciNet): MR290982
Zentralblatt MATH: 0313.05003
J. Koh, Ideals generated by quadrics exhibiting double exponential degrees, J. Algebra 200 (1998), 225--245.
Mathematical Reviews (MathSciNet): MR1603272
Zentralblatt MATH: 0924.13022
Digital Object Identifier: doi:10.1006/jabr.1997.7225
J. Kruskal, The number of simplices in a complex, Mathematical Optimization Techniques (R. Bellman, ed.), University of California Press, Berkeley/Los Angeles (1963), 251--278. \vfill
Mathematical Reviews (MathSciNet): MR154827
Zentralblatt MATH: 0116.35102
R. Lazarsfeld, A sharp Castelnuovo bound for smooth surfaces, Duke Math. J. 55 (1987), 423-429.
Mathematical Reviews (MathSciNet): MR894589
Zentralblatt MATH: 0646.14005
Digital Object Identifier: doi:10.1215/S0012-7094-87-05523-2
Project Euclid: euclid.dmj/1077306029
F. Macaulay, Some properties of enumeration in the theory of modular systems, Proc. London Math. Soc. 26 (1927), 531-555.
D. Maclagan, and G. Smith, Multigraded Castelnuovo-Mumford regularity, J. Reine Angew. Math. 571 (2004), 179-212.
Mathematical Reviews (MathSciNet): MR2070149
E. Mayr and A. Meyer, The complexity of the word problems for commutative semigroups and polynomial ideals, Adv. Math. 46 (1982), 305-329.
Mathematical Reviews (MathSciNet): MR683204
Zentralblatt MATH: 0506.03007
Digital Object Identifier: doi:10.1016/0001-8708(82)90048-2
J. Mermin and S. Murai, The lex-plus-powers conjecture holds for pure powers, submitted.
J. Mermin and I. Peeva, Hilbert functions and lex ideals, J. Algebra, 313 (2007), 642-656.
Mathematical Reviews (MathSciNet): MR2329561
Zentralblatt MATH: 05166802
Digital Object Identifier: doi:10.1016/j.jalgebra.2007.03.036
J. Migliore, The geometry of Hilbert functions, Syzygies and Hilbert functions, I. Peeva editor, Lect. Notes Pure Appl. Math. 254 (2007), CRC Press.
Mathematical Reviews (MathSciNet): MR2309930
Zentralblatt MATH: 1145.13010
J. Migliore, U. Nagel, Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers, Adv. Math. 180 (2003), 1-63.
Mathematical Reviews (MathSciNet): MR2019214
Zentralblatt MATH: 1053.13006
Digital Object Identifier: doi:10.1016/S0001-8708(02)00079-8
U. Nagel and V. Reiner, Betti numbers of monomial ideals and shifted skew shapes, preprint.
P. Orlik and H. Terao, Arrangements of Hyperplanes, Springer-Verlag, (1992).
Mathematical Reviews (MathSciNet): MR1217488
G. Ottaviani and R. Paoletti, Syzygies of Veronese embeddings, Compositio Math. 125 (2001), 31-37.
Mathematical Reviews (MathSciNet): MR1818055
Zentralblatt MATH: 0999.14016
Digital Object Identifier: doi:10.1023/A:1002662809474
I. Peeva, Syzygies and Hilbert functions, Lect. Notes Pure Appl. Math. 254 (2007), CRC Press.
Mathematical Reviews (MathSciNet): MR2309924
--------, Hyperplane arrangements and linear strands in resolutions, Trans. Amer. Math. Soc. 355 (2003), 609-618.
Mathematical Reviews (MathSciNet): MR1932716
Zentralblatt MATH: 1084.52520
Digital Object Identifier: doi:10.1090/S0002-9947-02-03128-8
JSTOR: links.jstor.org
I. Peeva, V. Reiner and V. Welker, Cohomology of real diagonal subspace arrangements via resolutions, Compositio Mathematica 117 (1999), 107-123.
Mathematical Reviews (MathSciNet): MR1693007
Zentralblatt MATH: 0954.13006
Digital Object Identifier: doi:10.1023/A:1000949217231
I. Peeva and M. Stillman, Toric Hilbert schemes, Duke Math. J. 111 (2002), 419-449.
Mathematical Reviews (MathSciNet): MR1885827
Zentralblatt MATH: 1067.14005
Digital Object Identifier: doi:10.1215/S0012-7094-02-11132-6
Project Euclid: euclid.dmj/1087575081
M. Ramras, Sequences of Betti numbers, J. Algebra 66 (1980), 193-204.
Mathematical Reviews (MathSciNet): MR591252
Zentralblatt MATH: 0474.13007
Digital Object Identifier: doi:10.1016/0021-8693(80)90119-2
Z. Ran, Local differential geometry and generic projections of threefolds, J. Differential Geom. 32 (1990), 131--137.
Mathematical Reviews (MathSciNet): MR1064868
Zentralblatt MATH: 0788.14037
Project Euclid: euclid.jdg/1214445040
V. Reiner and V. Welker, On the Charney-Davis and Neggers-Stanley conjectures, J. Combin. Theory Ser. A 109 (2005), 247-280.
Mathematical Reviews (MathSciNet): MR2121026
Zentralblatt MATH: 1065.06002
Digital Object Identifier: doi:10.1016/j.jcta.2004.09.003
B. Richert, Smallest graded Betti numbers, J. Algebra 244 (2001), 236-259.
Mathematical Reviews (MathSciNet): MR1856536
Zentralblatt MATH: 1027.13008
Digital Object Identifier: doi:10.1006/jabr.2001.8878
L. Robiano, COCOA\thinspace--\thinspacea system for computation in algebraic geometry and commutative algebra, (1997), available from http://cocoa.dima.unige.it/.
J.-E. Roos, Commutative non Koszul algebras having a linear resolution of arbitrary high order. Applications to torsion in loop space homology, C. R. Acad. Sci. Paris Sér. I 316 (1993), 1123-1128.
Mathematical Reviews (MathSciNet): MR1221635
H. Schenck, M. Stillman, High rank linear syzygies on low rank quadrics, preprint.
H. Schenck, A. Suciu, Resonance, linear syzygies, Chen groups, and the Bernstein-Gelfand-Gelfand correspondence, Trans. Amer. Math. Soc. 358 (2006), 2269--2289.
Mathematical Reviews (MathSciNet): MR2197444
Zentralblatt MATH: 1153.52008
Digital Object Identifier: doi:10.1090/S0002-9947-05-03853-5
J. Sidman, A. Van Tuyl and H. Wang, Multigraded regularity: coarsenings and resolutions, J. Algebra 301 (2006), 703-727.
Mathematical Reviews (MathSciNet): MR2236764
Zentralblatt MATH: 1113.14034
Digital Object Identifier: doi:10.1016/j.jalgebra.2005.09.032
R. Stanley, Positivity problems and conjectures in algebraic combinatorics, in Mathematics: frontiers and perspectives, Amer. Math. Soc., Providence, RI, (2000), 295--319,.
Mathematical Reviews (MathSciNet): MR1754784
Zentralblatt MATH: 0955.05111
--------, Log-concave and unimodal sequences in algebra, combinatorics, and geometry, Graph theory and its applications: East and West (Jinan, 1986), Ann. New York Acad. Sci. 576, New York Acad. Sci., New York, (1989), 500--535.
Mathematical Reviews (MathSciNet): MR1110850
Zentralblatt MATH: 0792.05008
--------, Combinatorics and commutative algebra, Progress in Mathematics 41, Birkh�user Boston, Inc., Boston, MA, (1996).
Mathematical Reviews (MathSciNet): MR1453579
A. Suciu, Fundamental groups of line arrangements: Enumerative aspects, Advances in algebraic geometry motivated by physics, Contemporary Math., 276, (2001), Amer. Math. Soc., 43-79.
Mathematical Reviews (MathSciNet): MR1837109
Zentralblatt MATH: 0998.14012
I. Swanson, On the embedded primes of the Mayr-Meyer ideals, J. Algebra 275 (2004), 143-190.
Mathematical Reviews (MathSciNet): MR2047444
Zentralblatt MATH: 1082.13015
Digital Object Identifier: doi:10.1016/j.jalgebra.2003.11.016
--------, Multigraded Hilbert functions and mixed multiplicities, Syzygies and Hilbert functions, Lect. Notes Pure Appl. Math. 254, Chapman & Hall/CRC, Boca Raton, FL, (2007), 267-280.
Mathematical Reviews (MathSciNet): MR2309934
Zentralblatt MATH: 1145.13012
N. Terai, Alexander duality in Stanley-Reisner rings, Affine algebraic geometry, Osaka Univ. Press, Osaka, (2007), 449-462.
Mathematical Reviews (MathSciNet): MR2330484
Zentralblatt MATH: 1128.13014
G. Valla, Hilbert functions of graded algebras, Six lectures on commutative algebra (Bellaterra, 1996), Progr. Math., 166, Birkh�user, Basel, (1998), 293-344.
Mathematical Reviews (MathSciNet): MR1648668
Zentralblatt MATH: 0946.13012
V. Welker, Discrete Morse theory and free resolutions, Algebraic combinatorics, Universitext, Springer, Berlin, (2007), 81-172.
Mathematical Reviews (MathSciNet): MR2321838
Zentralblatt MATH: 1128.13007
previous :: next
Journal of Commutative Algebra
