# zbMATH — the first resource for mathematics

Restriction of hypergeometric $$\mathcal{D}$$-modules with respect to coordinate subspaces. (English) Zbl 1232.13016
The authors determine the restriction of an $$A$$-hypergeometric $$D$$-module with respect to a coordinate subspace, under rather strong genericity conditions.

##### MSC:
 13N10 Commutative rings of differential operators and their modules 14D99 Families, fibrations in algebraic geometry
##### Keywords:
hypergeometric $$D$$-module
Full Text:
##### References:
 [1] Francisco Jesús Castro-Jiménez and Nobuki Takayama, Singularities of the hypergeometric system associated with a monomial curve, Trans. Amer. Math. Soc. 355 (2003), no. 9, 3761 – 3775. · Zbl 1060.33023 [2] María-Cruz Fernández-Fernández and Francisco Jesús Castro-Jiménez, Gevrey solutions of the irregular hypergeometric system associated with an affine monomial curve, Trans. Amer. Math. Soc. 363 (2011), no. 2, 923-948. · Zbl 1219.32007 [3] I. M. Gel$$^{\prime}$$fand, M. I. Graev, and A. V. Zelevinskiĭ, Holonomic systems of equations and series of hypergeometric type, Dokl. Akad. Nauk SSSR 295 (1987), no. 1, 14 – 19 (Russian); English transl., Soviet Math. Dokl. 36 (1988), no. 1, 5 – 10. [4] I. M. Gel$$^{\prime}$$fand, A. V. Zelevinskiĭ, and M. M. Kapranov, Hypergeometric functions and toric varieties, Funktsional. Anal. i Prilozhen. 23 (1989), no. 2, 12 – 26 (Russian); English transl., Funct. Anal. Appl. 23 (1989), no. 2, 94 – 106. · Zbl 0721.33006 [5] Yves Laurent and Zoghman Mebkhout, Image inverse d’un \?-module et polygone de Newton, Compositio Math. 131 (2002), no. 1, 97 – 119 (French, with English summary). · Zbl 0993.35007 [6] Laura Felicia Matusevich, Ezra Miller, and Uli Walther, Homological methods for hypergeometric families, J. Amer. Math. Soc. 18 (2005), no. 4, 919 – 941. · Zbl 1095.13033 [7] Philippe Maisonobe and Tristan Torrelli, Image inverse en théorie des \?-modules, Éléments de la théorie des systèmes différentiels géométriques, Sémin. Congr., vol. 8, Soc. Math. France, Paris, 2004, pp. 1 – 57 (French, with English and French summaries). · Zbl 1062.32009 [8] Toshinori Oaku, Algorithms for \?-functions, restrictions, and algebraic local cohomology groups of \?-modules, Adv. in Appl. Math. 19 (1997), no. 1, 61 – 105. · Zbl 0938.32005 [9] Toshinori Oaku and Nobuki Takayama, Algorithms for \?-modules — restriction, tensor product, localization, and local cohomology groups, J. Pure Appl. Algebra 156 (2001), no. 2-3, 267 – 308. · Zbl 0983.13008 [10] Mutsumi Saito, Isomorphism classes of \?-hypergeometric systems, Compositio Math. 128 (2001), no. 3, 323 – 338. · Zbl 1075.33009 [11] Bernd Sturmfels and Nobuki Takayama, Gröbner bases and hypergeometric functions, Gröbner bases and applications (Linz, 1998) London Math. Soc. Lecture Note Ser., vol. 251, Cambridge Univ. Press, Cambridge, 1998, pp. 246 – 258. · Zbl 0918.33004 [12] Mathias Schulze and Uli Walther, Hypergeometric D-modules and twisted Gauß-Manin systems, J. Algebra 322 (2009), no. 9, 3392 – 3409. · Zbl 1181.13023 [13] Uli Walther, Duality and monodromy reducibility of \?-hypergeometric systems, Math. Ann. 338 (2007), no. 1, 55 – 74. · Zbl 1126.33006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.