Duke Mathematical Journal
previous :: next

Binomial ideals

David Eisenbud and Bernd Sturmfels
Source: Duke Math. J. Volume 84, Number 1 (1996), 1-45.
First Page: Show Hide
Primary Subjects: 13P10
Secondary Subjects: 13A30, 14M25
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.dmj/1077243627
Mathematical Reviews number (MathSciNet): MR1394747
Zentralblatt MATH identifier: 0873.13021
Digital Object Identifier: doi:10.1215/S0012-7094-96-08401-X

References

[A] V. I. Arnold, $A$-graded algebras and continued fractions, Comm. Pure Appl. Math. 42 (1989), no. 7, 993–1000.
Mathematical Reviews (MathSciNet): MR90h:32025
Zentralblatt MATH: 0692.16012
Digital Object Identifier: doi:10.1002/cpa.3160420705
[BS] D. Bayer and M. Stillman, On the complexity of computing syzygies, J. Symbolic Comput. 6 (1988), no. 2-3, 135–147.
Mathematical Reviews (MathSciNet): MR90g:68071
Zentralblatt MATH: 0667.68053
Digital Object Identifier: doi:10.1016/S0747-7171(88)80039-7
[BGN] E. Becker, R. Grobe, and M. Niermann, Real zeros and real radicals of binomial ideals, manuscript, 1996.
Mathematical Reviews (MathSciNet): MR1457832
Zentralblatt MATH: 0889.13001
Digital Object Identifier: doi:10.1016/S0022-4049(97)00004-2
[Br] W. D. Brownawell, Bounds for the degrees in the Nullstellensatz, Ann. of Math. (2) 126 (1987), no. 3, 577–591.
Mathematical Reviews (MathSciNet): MR89b:12001
Zentralblatt MATH: 0641.14001
Digital Object Identifier: doi:10.2307/1971361
[Bu] B. Buchberger, Gröbner bases: an algorithmic method in polynomial ideal theory, Multidimensional Systems Theory, Math. Appl., vol. 16, D. Reidel, Dordrecht, 1985.
Zentralblatt MATH: 0587.13009
[BE] D. Buchsbaum and D. Eisenbud, Generic free resolutions and a family of generically perfect ideals, Advances in Math. 18 (1975), no. 3, 245–301.
Mathematical Reviews (MathSciNet): MR53:391
Zentralblatt MATH: 0336.13007
Digital Object Identifier: doi:10.1016/0001-8708(75)90046-8
[VR] D. Buchsbaum and D. S. Rim, A generalized Koszul complex. II. Depth and multiplicity, Trans. Amer. Math. Soc. 111 (1964), 197–224.
Mathematical Reviews (MathSciNet): MR28:3076
Zentralblatt MATH: 0131.27802
Digital Object Identifier: doi:10.2307/1994241
[CT] P. Conti and C. Traverso, Buchberger algorithm and integer programming, Applied algebra, algebraic algorithms and error-correcting codes (New Orleans, LA, 1991), Lecture Notes in Comput. Sci., vol. 539, Springer, Berlin, 1991, pp. 130–139.
Mathematical Reviews (MathSciNet): MR1229314
Zentralblatt MATH: 0771.13014
[CLO] D. Cox, J. Little, and D. O'Shea, Ideals, varieties, and algorithms, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1992.
Mathematical Reviews (MathSciNet): MR93j:13031
Zentralblatt MATH: 0756.13017
[DMS] W. Decker, N. Manolache, and F. Schreyer, Geometry of the Horrocks bundle on $\bf P\sp 5$, Complex projective geometry (Trieste, 1989/Bergen, 1989), London Math. Soc. Lecture Note Ser., vol. 179, Cambridge Univ. Press, Cambridge, 1992, pp. 128–148.
Mathematical Reviews (MathSciNet): MR94h:14043
Zentralblatt MATH: 0774.14013
[DS] P. Diaconis and B. Sturmfels, Algebraic algorithms for generating from conditional distributions, to appear in Ann. Statist.
Mathematical Reviews (MathSciNet): MR1608156
Zentralblatt MATH: 0952.62088
Digital Object Identifier: doi:10.1214/aos/1030563990
Project Euclid: euclid.aos/1030563990
[E] D. Eisenbud, Commutative algebra with a View Toward Algebraic Geometry, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995.
Mathematical Reviews (MathSciNet): MR97a:13001
Zentralblatt MATH: 0819.13001
[EHV] D. Eisenbud, C. Huneke, and W. Vasconcelos, Direct methods for primary decomposition, Invent. Math. 110 (1992), no. 2, 207–235.
Mathematical Reviews (MathSciNet): MR93j:13032
Zentralblatt MATH: 0770.13018
Digital Object Identifier: doi:10.1007/BF01231331
[ES] D. Eisenbud and B. Sturmfels, Finding sparse systems of parameters, J. Pure Appl. Algebra 94 (1994), no. 2, 143–157.
Mathematical Reviews (MathSciNet): MR95i:13020
Zentralblatt MATH: 0807.13012
Digital Object Identifier: doi:10.1016/0022-4049(94)90029-9
[F] W. Fulton, Introduction to toric varieties, Annals of Mathematics Studies, vol. 131, Princeton University Press, Princeton, NJ, 1993.
Mathematical Reviews (MathSciNet): MR94g:14028
Zentralblatt MATH: 0813.14039
[GTZ] P. Gianni, B. Trager, and G. Zacharias, Gröbner bases and primary decomposition of polynomial ideals, J. Symbolic Comput. 6 (1988), no. 2-3, 149–167.
Mathematical Reviews (MathSciNet): MR90f:68091
Zentralblatt MATH: 0667.13008
Digital Object Identifier: doi:10.1016/S0747-7171(88)80040-3
[Gi] R. Gilmer, Commutative semigroup rings, Chicago Lectures in Math., University of Chicago Press, Chicago, IL, 1984.
Mathematical Reviews (MathSciNet): MR85e:20058
Zentralblatt MATH: 0566.20050
[H] I. Hoveijn, Aspects of resonance in dynamical systems, Ph.D. thesis, University of Utrecht, Netherlands, 1992.
[Kol] J. Kollár, Sharp effective Nullstellensatz, J. Amer. Math. Soc. 1 (1988), no. 4, 963–975.
Mathematical Reviews (MathSciNet): MR89h:12008
Zentralblatt MATH: 0682.14001
Digital Object Identifier: doi:10.2307/1990996
[Kor] E. Korkina, Classification of $A$-graded algebras with $3$ generators, Indag. Math. (N.S.) 3 (1992), no. 1, 27–40.
Mathematical Reviews (MathSciNet): MR93c:13013
Zentralblatt MATH: 0756.13011
Digital Object Identifier: doi:10.1016/0019-3577(92)90025-G
[KPR] E. Korkina, G. Post, and M. Roelofs, Algèbres graduées de type $A$, C. R. Acad. Sci. Paris Sér. I Math. 314 (1992), no. 9, 653–655.
Mathematical Reviews (MathSciNet): MR92m:16061
Zentralblatt MATH: 0761.13002
[L] S. Lang, Algebra, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965.
Mathematical Reviews (MathSciNet): MR33:5416
Zentralblatt MATH: 0193.34701
[MM] E. Mayr and A. Meyer, The complexity of the word problems for commutative semigroups and polynomial ideals, Adv. in Math. 46 (1982), no. 3, 305–329.
Mathematical Reviews (MathSciNet): MR84g:20099
Zentralblatt MATH: 0506.03007
Digital Object Identifier: doi:10.1016/0001-8708(82)90048-2
[RS] L. Robbiano and M. Sweedler, Subalgebra bases, Commutative algebra (Salvador, 1988), Lecture Notes in Math., vol. 1430, Springer, Berlin, 1990, pp. 61–87.
Mathematical Reviews (MathSciNet): MR91f:13027
Zentralblatt MATH: 0725.13013
Digital Object Identifier: doi:10.1007/BFb0085537
[Sta] R. Stanley, Generalized $H$-vectors, intersection cohomology of toric varieties, and related results, Commutative algebra and combinatorics (Kyoto, 1985), Adv. Stud. Pure Math., vol. 11, North-Holland, Amsterdam, 1987, pp. 187–213.
Mathematical Reviews (MathSciNet): MR89f:52016
Zentralblatt MATH: 0652.52007
[Stu1] B. Sturmfels, Gröbner bases of toric varieties, Tohoku Math. J. (2) 43 (1991), no. 2, 249–261.
Mathematical Reviews (MathSciNet): MR92j:14067
Zentralblatt MATH: 0714.14034
Digital Object Identifier: doi:10.2748/tmj/1178227496
Project Euclid: euclid.tmj/1178227496
[Stu2] B. Sturmfels, Asymptotic analysis of toric ideals, Mem. Fac. Sci. Kyushu Univ. Ser. A 46 (1992), no. 2, 217–228.
Mathematical Reviews (MathSciNet): MR93k:14070
Zentralblatt MATH: 0784.14024
Digital Object Identifier: doi:10.2206/kyushumfs.46.217
[T] R. Thomas, A geometric Buchberger algorithm for integer programming, to appear in Math. Oper. Res.
Mathematical Reviews (MathSciNet): MR1378110
Zentralblatt MATH: 0846.90079
Digital Object Identifier: doi:10.1287/moor.20.4.864
[X] S. Xambó, On projective varieties of minimal degree, Collect. Math. 32 (1981), no. 2, 149–163.
Mathematical Reviews (MathSciNet): MR84e:14039
Zentralblatt MATH: 0501.14020
[Y] C. K. Yap, A new lower bound construction for commutative Thue systems with applications, J. Symbolic Comput. 12 (1991), no. 1, 1–27.
Mathematical Reviews (MathSciNet): MR92i:03046
Zentralblatt MATH: 0731.68060
Digital Object Identifier: doi:10.1016/S0747-7171(08)80138-1
previous :: next

2012 © Duke University Press

Duke Mathematical Journal

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?