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A-Hypergeometric Systems and Relative Cohomology
International Journal of Mathematics  (IF0.688),  Pub Date : 2020-11-11, DOI: 10.1142/s0129167x2050113x
Tsung-Ju Lee, Dingxin Zhang

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.