Homology and cohomology intersection numbers of GKZ systems

被引：4

作者：

Goto, Yoshiaki ^{[1
]}

Matsubara-Heo, Saiei-Jaeyeong ^{[2
]}

机构：

[1] Otaru Univ, Gen Educ, 3-5-21 Midori, Otaru, Hokkaido 0478501, Japan

[2] Kobe Univ, Grad Sch Sci, Nada Ku, 1-1 Rokkodai, Kobe, Hyogo 6578501, Japan

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 2022年 / 33卷 / 03期

关键词：

GKZ system; Twisted (co)homology group; Intersection theory; Monodromy invariant hermitian form; HYPERGEOMETRIC-FUNCTIONS; MULTIFORM FUNCTIONS; LINEAR DIFFERENCES; TWISTED CYCLES; INTEGRALS; MONODROMY; EQUATIONS;

D O I：

10.1016/j.indag.2021.12.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe the homology intersection form associated to regular holonomic GKZ systems in terms of the combinatorics of regular triangulations. Combining this result with the twisted period relation, we obtain a formula of cohomology intersection numbers in terms of a Laurent series. We show that the cohomology intersection number depends rationally on the parameters. We also prove a conjecture of F. Beukers and C. Verschoor on the signature of the monodromy invariant hermitian form. (C) 2021 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

引用

页码：546 / 580

页数：35

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