Hypergeometric functions for projective toric curves. (English) Zbl 1350.32006
The authors study the behavior of the solutions of the A-hypergeometric system associated to a projective monomial curve as the parameters vary. They introduce extended Euler-Mellin integrals, then they study their behavior for parameters that are resonant with respect to precisely one faset of A. They understand the behavior of these solutions along a line in poles while the behavior along nonpolar lines is different. Also they explain the behavior of extended Euler-Mellin integrals at parameters that lie at the intersection of two resonant lines. Finally they discuss how hypergeometric solutions at rank jumps are connected to local cohomology and all the ideas are illustrated by an example.
Reviewer: Chrysoula G. Kokologiannaki (Patras)
MSC:
| 32A17 | Special families of functions of several complex variables |
| 33C70 | Other hypergeometric functions and integrals in several variables |
| 14M25 | Toric varieties, Newton polyhedra, Okounkov bodies |
| 14F10 | Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials |
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