English

$A$-hypergeometric systems and relative cohomology

Algebraic Geometry 2020-11-18 v3

Abstract

We investigate the space of solutions to certain AA-hypergeometric D\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 AA, 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.

Keywords

Cite

@article{arxiv.1902.01536,
  title  = {$A$-hypergeometric systems and relative cohomology},
  author = {Tsung-Ju Lee and Dingxin Zhang},
  journal= {arXiv preprint arXiv:1902.01536},
  year   = {2020}
}

Comments

18 pages. Comments are welcome! In this version, we corrected statements in Lemma 1.8 and Lemma 4.8

R2 v1 2026-06-23T07:32:09.954Z