Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
Full text of review:
PDF
This review is available free of charge.
Book Information:
Authors:
M. Saito,
B. Sturmfels and
N. Takayama
Title:
Gröbner deformations of hypergeometric differential equations
Additional book information:
Springer,
New York,
2000,
viii+254 pp.,
ISBN 3-540-66065-8,
$42.00$
[1] D. Cox, J. Little, D. O'Shea, Ideals, Varieties and Algorithms, Springer, 1992. MR 1189133
[2] W. Fulton, Introduction to Toric Varieties, Princeton Univ. Press, 1993. MR 1234037
[3] I.M. Gelfand, General theory of hypergeometric functions, Sov. Math. Dokl. 33 (1986), 573-577. MR 0841131
[4] I.M. Gelfand, S.I. Gelfand, Generalized hypergeometric equations, Sov. Math. Dokl. 33 (1986), 643-646. MR 0843436
[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 0902936
[6] I.M. Gelfand, M.M. Kapranov, A.V. Zelevinsky, Generalized Euler integrals and A-hypergeometric functions, Adv. Math. 84 (1990), 255-271. MR 1080980
[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 1011353; 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 1461942
[9] S. Hosono, B. Lian, S.-T. Yau, Maximal degeneracy points of GKZ systems, Journal of the AMS 10 (1997), 427-443. MR 1423031
[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 1672077
[11] B. Sturmfels, Gröbner Bases and Convex Polytopes, Amer. Math. Soc., 1996. MR 1363949
[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 1708882
- [1]
- D. Cox, J. Little, D. O'Shea, Ideals, Varieties and Algorithms, Springer, 1992. MR 1189133
- [2]
- W. Fulton, Introduction to Toric Varieties, Princeton Univ. Press, 1993. MR 1234037
- [3]
- I.M. Gelfand, General theory of hypergeometric functions, Sov. Math. Dokl. 33 (1986), 573-577. MR 0841131
- [4]
- I.M. Gelfand, S.I. Gelfand, Generalized hypergeometric equations, Sov. Math. Dokl. 33 (1986), 643-646. MR 0843436
- [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 0902936
- [6]
- I.M. Gelfand, M.M. Kapranov, A.V. Zelevinsky, Generalized Euler integrals and A-hypergeometric functions, Adv. Math. 84 (1990), 255-271. MR 1080980
- [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 1011353; 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 1461942
- [9]
- S. Hosono, B. Lian, S.-T. Yau, Maximal degeneracy points of GKZ systems, Journal of the AMS 10 (1997), 427-443. MR 1423031
- [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 1672077
- [11]
- B. Sturmfels, Gröbner Bases and Convex Polytopes, Amer. Math. Soc., 1996. MR 1363949
- [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 1708882
Review Information:
Reviewer:
Mikhail Kapranov
Affiliation:
University of Toronto
Email:
kapranov@math.toronto.edu
Journal:
Bull. Amer. Math. Soc.
38 (2001), 481-488
Published electronically:
June 12, 2001
Review copyright:
© Copyright 2001
American Mathematical Society
