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arXiv · 1902.01536

$A$-hypergeometric systems and relative cohomology

Tsung-Ju Lee·Dingxin Zhang
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Abstract

We investigate the space of solutions to certain $A$-hypergeometric $\mathscr{D}$-modules, which were defined and studied by Gelfand, Kapranov, and Zelevinsky. We show that the solution space can be identified with certain relative cohomology group of the toric variety determined by $A$, which generalizes the results of Huang, Lian, Yau, and Zhu. As a corollary, we also prove the existence of rank one points for Calabi--Yau complete intersections in toric varieties.

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Tsung-Ju Lee, Dingxin Zhang. 2019-02-05. $A$-hypergeometric systems and relative cohomology. https://arxiv.org/abs/1902.01536

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