Pfaffian of Appell's hypergeometric system F₄ in terms of the intersection form of twisted cohomology groups

2015/02/03 by Yoshiaki Gotō, Goto, Yoshiaki, Jyoichi Kaneko +3
Computer Science · Engineering · Physics and Astronomy · #33C65 #58A17 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1502.00795

openalex publication_date 2015/02/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study a Pfaffian of the system of differential equations annihilating Appell's hypergeometric series F₄(a,b,c;x) by twisted cohomology groups associated with integrals representing solutions to this system. We simplify its connection matrix by the pull-back under a double cover of the complement of the singular locus. We express the simplified connection matrix in terms of the intersection form of the twisted cohomology groups.

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