Pfaffian of Appell's Hypergeometric System $\mathcal F_4$ in Terms of the Intersection Form of Twisted Cohomology Groups
Yoshiaki Gotō, Jyoichi Kaneko, Keiji Matsumoto · Publications of the Research Institute for Mathematical Sciences · 2016
We study a Pfaffian of Appell's hypergeometric system \mathcal F_4 (a,b,c) of differential equations by twisted cohomology groups associated with Euler type integrals representing solutions. 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 between the twisted cohomology groups.