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Book Review
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Book Information
Author(s):
M. Saito, B. Sturmfels and N. Takayama
Title:
Gröbner deformations of hypergeometric differential equations
Additional book information:
Springer,
New York,
2000,
viii+254 pp.,
$42.00,
ISBN 3-540-66065-8
References:
- [1]
- D. Cox, J. Little, D. O'Shea, Ideals, Varieties and Algorithms, Springer, 1992. MR 93j:13031
- [2]
- W. Fulton, Introduction to Toric Varieties, Princeton Univ. Press, 1993. MR 94g:14028
- [3]
- I.M. Gelfand, General theory of hypergeometric functions, Sov. Math. Dokl. 33 (1986), 573-577. MR 87h:22012
- [4]
- I.M. Gelfand, S.I. Gelfand, Generalized hypergeometric equations, Sov. Math. Dokl. 33 (1986), 643-646. MR 87h:22013
- [5]
- I.M. Gelfand, M.I. Graev, A.V. Zelevinsky, Holonomic systems of equations and series of hypergeometric type, Soviet Math. Dokl. 36 (1988), 5-10. MR 88j:58118
- [6]
- I.M. Gelfand, M.M. Kapranov, A.V. Zelevinsky, Generalized Euler integrals and A-hypergeometric functions, Adv. Math. 84 (1990), 255-271. MR 92e:33015
- [7]
- I.M. Gelfand, A.V. Zelevinsky, M.M. Kapranov, Hypergeometric functions and toric varieties, Funct. Anal. Appl. 23 (1989), 94-106; see also correction, ibid. 27 (1993), 295. MR 90m:22025; MR 95a:22010
- [8]
- S. Hosono, B. Lian, S.-T. Yau, GKZ-generalized hypergeometric functions in mirror symmetry of Calabi-Yau hypersurfaces, Comm. Math. Phys. 182 (1996), 535-577. MR 98g:14042
- [9]
- S. Hosono, B. Lian, S.-T. Yau, Maximal degeneracy points of GKZ systems, Journal of the AMS 10 (1997), 427-443. MR 97j:32014
- [10]
- J. Stienstra, Resonant hypergeometric systems and mirror symmetry, in: ``Integrable Systems and Algebraic Geometry" (Proceedings of the Taniguchi Symposium 1997, M.-H. Saito, Y. Shimizu, K. Ueno, Eds.), World Scientific, 1998. MR 2000b:14013
- [11]
- B. Sturmfels, Gröbner Bases and Convex Polytopes, Amer. Math. Soc., 1996. MR 97b:13034
- [12]
- B. Sturmfels, N. Takayama, Gröbner bases and hypergeometric functions, in: ``Gröbner Bases and Applications" (Linz, 1998), pp. 246-258, London Math. Soc. Lect. Series 251, Cambridge Univ. Press, 1998. MR 2001c:33026
Additional Information:
Reviewer(s):
Mikhail
Kapranov
Affiliation:
University of Toronto
Email:
kapranov@math.toronto.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
38
(2001),
481-488.
MSC
(2000):
Primary 13P10, 14Qxx, 16S32, 33Cxx, 34Exx, 35Axx, 68W30
PII:
S 0273-0979(01)00915-6
Posted:
June 12, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
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