Pfaffian of Appell's Hypergeometric System $\mathcal F_4$ in Terms of the Intersection Form of Twisted Cohomology Groups

Yoshiaki Goto; Jyoichi Kaneko; Keiji Matsumoto

doi:10.4171/prims/179

Pfaffian of Appell's Hypergeometric System $F_{4}$ in Terms of the Intersection Form of Twisted Cohomology Groups

Yoshiaki Goto
Kobe University, Japan
Jyoichi Kaneko
University of the Ryukyus, Okinawa, Japan
Keiji Matsumoto
Hokkaido University, Sapporo, Japan

$Pfaffian of Appell's Hypergeometric System $\mathcal F_4$ in Terms of the Intersection Form of Twisted Cohomology Groups cover$

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Abstract

We study a Pfaffian of Appell's hypergeometric system $F_{4} (a, b, c)$ 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.

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Yoshiaki Goto, Jyoichi Kaneko, Keiji Matsumoto, Pfaffian of Appell's Hypergeometric System $F_{4}$ in Terms of the Intersection Form of Twisted Cohomology Groups. Publ. Res. Inst. Math. Sci. 52 (2016), no. 2, pp. 223–247

DOI 10.4171/PRIMS/179