Singularities of the hypergeometric system associated with a monomial curve

Transactions of the American Mathematical Society

Volumn 355, Issue 9, 2003, Pages 3761-3775

  Castro Jiménez, Francisco Jesús ^a   Takayama, Nobuki ^b  

^a UNIVERSITY OF SEVILLE   (Spain)

^b KOBE UNIVERSITY   (Japan)

Author keywords

Algebraic geometry; D modules; Hypergeometric systems; Toric varieties

Indexed keywords

EID: 0041862808     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-03-03300-2     Document Type: Article

References (19)

1. Adolphson, A., Hypergeometric functions and rings generated by monomials, Duke Mathematical Journal 73 (1994), 269-290. MR 96c:33020
2. Assi, A., Castro-Jiménez, F. J., and Granger, J. M., How to calculate the slopes of a D-module, Compositio Math. 104 (1996), no. 2, 107-123. MR 98i:32010
3. n-module, J. Pure Appl. Algebra 150 (2000), 1, 27-39. MR 2001j:16036
4. Beukers, F., Brownawell, W. D., and Heckman, G., Siegel normality, Ann. of Math. (2) 127 (1988), no. 2, 279-308. MR 90e:11106
5. Cattani, E., D'Andrea, C., and Dickenstein, A., The A-hypergeometric system associated with a monomial curve, Duke Mathematical J. 99 (1999), 179-207. MR 2001f:33018
6. Gel'fand, I. M., Zelevinskiǐ, A. V., and Kapranov, M. M., Hypergeometric functions and toric varieties, Funktsional. Anal, i Prilozhen., 23 (1989), 2, 12-26; English transl., Funct. Anal. Appl. 23 (1989), no. 2, 94-106. MR 90m:22025
7. Gel'fand, I. M., Zelevinskiǐ, A. V., and Kapranov, M. M., Hypergeometric functions and toric varieties, Funktsional. Anal, i Prilozhen., 23 (1989), 2, 12-26; English transl., Funct. Anal. Appl. 23 (1989), no. 2, 94-106. MR 90m:22025
8. Grayson, D. and Stillman, M., Macaulay2, a software system for research in algebraic geometry, available at http://www.math.uiuc.edu/Macaulay2.
9. Hotta, R., Equivariant D-modules. Preprint math.RT/9805021.
10. Laurent, Y. Théorie de la deuxième microlocalisation dans le domaine complexe, Progress in Math. 53, Birkhäuser, 1985. MR 86k:58113
11. Laurent, Y., Polygone de Newton et b-fonctions pour les modules microdifférentiels, Ann. Sci. École Norm. Sup. (4) 20 (1987), no. 3, 391-441. MR 89k:58282
12. Laurent, Y. and Mebkhout, Z., Pentes algébriques et pentes analytiques d'un D-module, Ann. Sci. École Norm. Sup. (4) 32 (1999), no. 1, 39-69. MR 2001b:32015
13. Laurent, Y. and Mebkhout, Z., Image inverse d'un D-module et polygone de Newton, Compositio Math. 131 (2002), no. 1, 97-119.
14. Leykin, A. and Tsai, H., D-module package for Macaulay 2. http://www.math.Cornell.edu/̃htsai
15. X-modules, The Grothendieck Festschrift, Vol. III, 83-132, Progr. Math., 88, Birkhäuser, Boston, MA, 1990. MR 92j:32031
16. Oaku, T., Algorithms for b-functions, restriction and algebraic local cohomology groups of D-modules, Advances in Applied Mathematics 19 (1997), 61-105. MR 98d:14031
17. Oaku, T., Takayama, N., and Walther, U., A localization algorithm for D-modules, Journal of Symbolic Computation 29 (2000), 721-728. MR 2001g:13056
18. Saito, M., Sturmfels, B., and Takayama, N., Gröbner deformations of hypergeometric differential equations, Algorithms and Computation in Mathematics, 6. Springer-Verlag, Berlin, 2000. MR 2001i:13036
19. Takayama, N., Kan: A system for computation in algebraic analysis, 1991 version 1, 1994 version 2, the latest version is 3.000726. Source code available for Unix computers. Download from http://www.openxm.org