Gröbner bases of toric varieties
Bernd Sturmfels
Source: Tohoku Math. J. (2) Volume 43, Number 2
(1991), 249-261.
First Page:
Show
Hide
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.tmj/1178227496
Mathematical Reviews number (MathSciNet): MR1104431
Zentralblatt MATH identifier: 0714.14034
Digital Object Identifier: doi:10.2748/tmj/1178227496
References
[1] D BAYER AND I. MORRISON, Standard bases and geometric invariant theory I Initial ideals and state polytopes, J. Symbolic Computation 6 (1988), 209-217.
Mathematical Reviews (MathSciNet): MR988413
Zentralblatt MATH: 0675.13014
Digital Object Identifier: doi:10.1016/S0747-7171(88)80043-9
[2] D. BAYER AND I. MORRISON, Standard bases and geometric invariant theory II. A universally standar basis algorithm, presented at COCOA II, Geneva, May (1989).
[3] L J. BILLERA AND B. S MuNSON, Triangulations of oriented matroids and convex polytopes, SIAM Algebr Discrete Meth 5 (1984), 515-525
Mathematical Reviews (MathSciNet): MR763981
Zentralblatt MATH: 0557.05026
Digital Object Identifier: doi:10.1137/0605050
[4] L J. BILLERA, R CUSHMAN AND J. A. SANDERS, The Stanley decomposition of the harmonic oscillator, Proceedings Koninklijke Nederlandse Akademie van Wetenschappen 91 (1988), 375-393
Mathematical Reviews (MathSciNet): MR976522
Zentralblatt MATH: 0669.15006
[5] L J BILLERA, P FILLIMAN AND B. STURMFELS, Constructions and complexity of secondary polytopes, Advances in Mathematics, 82 (1990), 155-179
Mathematical Reviews (MathSciNet): MR1074022
Zentralblatt MATH: 0714.52004
Digital Object Identifier: doi:10.1016/0001-8708(90)90077-Z
[6] A BJORNER, M LAS VERGNAS, B STURMFELS, N. WHITE AND G. ZIEGLER, Oriented Matroids, to appear
Mathematical Reviews (MathSciNet): MR1226888
[7] B BUCHBERGER, Grobner bases–an algorithmic method inpolynomial ideal theory, Chapter 6 in N Bose (ed): "Multidimensional Systems Theory", D. Reidel, 1985
[8] V I DANILOV, The Geometry of Toric Varieties, Russian Math Surveys 33:2 (1978), 97-154; translate from Uspekhi Mat Nauk. 33:2 (1978), 85-134
Mathematical Reviews (MathSciNet): MR495499
Zentralblatt MATH: 0425.14013
[9] S. EILENBERG AND N. E SxEENROD, Foundations of Algebraic Topology, Princeton University Press, 1952
Mathematical Reviews (MathSciNet): MR50886
Zentralblatt MATH: 0047.41402
[10] I M GEL'FAND, M M KAPRANOV AND A. V ZELEVINSKY, Newton polytopes of principal j/ determinants, Soviet Math Doklady 308 (1989), 20-23.
[11] P. GRITZMANN AND B. STRUMFELS, Minkowski addition of polytopes: Computational complexity an applications to Grobner bases, Technical Report 90-12, MSI Cornell, 1990
[12] C LEE, Triangulating the /-cube, in "Discrete Geometry and Convexity", Annals of the New Yor Academy of Sciences 440 (1985), 205-211.
Mathematical Reviews (MathSciNet): MR809208
Zentralblatt MATH: 0574.52013
[13] C. LEE, Regular triangulations of convex polytopes, in "Applied Geometry and Discrete Mathematics-the Victor Klee Festschrift", (P Gritzmann and B Sturmfels, eds.), American Math Soc, Providence, to appear
Mathematical Reviews (MathSciNet): MR1116369
Zentralblatt MATH: 0746.52015
[14] E. MAYR AND A. MEYER, The complexity of the word problem for commutative semigroups an polynomial ideals, Advances in Math 46 (1982), 305-329.
Mathematical Reviews (MathSciNet): MR683204
Zentralblatt MATH: 0506.03007
Digital Object Identifier: doi:10.1016/0001-8708(82)90048-2
[15] T MORAANDL ROBBIANO, The Grobner fan of an ideal, Symbolic Computation 6 (1988), 183-20
Mathematical Reviews (MathSciNet): MR988412
Zentralblatt MATH: 0668.13017
Digital Object Identifier: doi:10.1016/S0747-7171(88)80042-7
[16] T ODA, Convex Bodies and Algebraic Geometry, an Introduction to the Theory of Toric Varieties, Springer-Verlag, Berlin, Heidelberg, New York, 1988
Mathematical Reviews (MathSciNet): MR922894
Zentralblatt MATH: 0628.52002
[17] R T ROCKAFELLAR, The elementary vectors of a subspace of /?", in: Combinatorial Mathematics an its Applications, (Proc Chapel Hill Conf.), Univ North Carolina Press, 1969, pp 104-127
Mathematical Reviews (MathSciNet): MR278972
Zentralblatt MATH: 0229.90019
[18] R P STANLEY, Combinatorics and Commutative Algebra, Birkhauser, Boston, 198
Mathematical Reviews (MathSciNet): MR725505
Zentralblatt MATH: 0537.13009
[19] R. P STANLEY, Decompositions of rational convex polytopes, Annals of Discrete Math. 6 (1980), 333-342
Mathematical Reviews (MathSciNet): MR593545
Zentralblatt MATH: 0812.52012
Digital Object Identifier: doi:10.1016/S0167-5060(08)70717-9
[20] B STURMFELS, Grobner bases and Stanley decompositions of determinantal rings, Mathematisch Zeitschrift, 205 (1990), 137-144
Mathematical Reviews (MathSciNet): MR1069489
Zentralblatt MATH: 0685.13005
Digital Object Identifier: doi:10.1007/BF02571229
[21] V WEISPFENNING, Constructing universal Grobner bases, in Proceedings AAEEC 5, Menorca 1987, Springer Lecture Notes in Computer Science 356, pp 408^17.
Mathematical Reviews (MathSciNet): MR1008554
Zentralblatt MATH: 0695.13002
Tohoku Mathematical Journal
