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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Irregular hypergeometric systems associated with a singular monomial curve
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by María Isabel Hartillo-Hermoso PDF
Trans. Amer. Math. Soc. 357 (2005), 4633-4646 Request permission


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:
  • Received by editor(s): July 15, 2003
  • Received by editor(s) in revised form: January 21, 2004
  • Published electronically: December 28, 2004
  • Additional Notes: This work was partially supported by FQM-813, FQM-333, DGESIC BFM2001-3164 and HF2000-0044
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 357 (2005), 4633-4646
  • MSC (2000): Primary 32C38; Secondary 13P10, 13N10, 33C80, 34M35
  • DOI:
  • MathSciNet review: 2156724