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Irregular hypergeometric systems associated with a singular monomial curve

Author(s): María Isabel Hartillo-Hermoso
Journal: Trans. Amer. Math. Soc. 357 (2005), 4633-4646.
MSC (2000): Primary 32C38; Secondary 13P10, 13N10, 33C80, 34M35
Posted: December 28, 2004
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Abstract: In this paper we study irregular hypergeometric systems defined by one row. Specifically, we calculate slopes of such systems. In the case of reduced semigroups, we generalize the case studied by Castro and Takayama. In all the cases we find that there always exists a slope with respect to a hyperplane of this system. Only in the case of an irregular system defined by a $1\times 2$integer matrix we might need a change of coordinates to study slopes at infinity. In the other cases slopes are always at the origin, defined with respect to a hyperplane. We also compute all the $L$-characteristic varieties of the system, so we have a section of the Gröbner fan of the module defined by the hypergeometric system.

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Additional Information:

María Isabel Hartillo-Hermoso
Affiliation: Departamento de Matemáticas, Universidad de Cádiz, Aptdo. 40, Puerto Real 11510 (Cádiz), Spain
Email: isabel.hartillo@uca.es

DOI: 10.1090/S0002-9947-04-03614-1
PII: S 0002-9947(04)03614-1
Keywords: ${\mathcal D}$-module, slopes, hypergeometric systems, Gr\"obner basis
Received by editor(s): July 15, 2003
Received by editor(s) in revised form: January 21, 2004
Posted: December 28, 2004
Additional Notes: This work was partially supported by FQM-813, FQM-333, DGESIC BFM2001-3164 and HF2000-0044
Copyright of article: Copyright 2004, American Mathematical Society

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