Relative twisted homology and cohomology groups associated with Lauricella's F_D

2018/04/02 by Keiji Matsumoto, Matsumoto, Keiji · 2 citations
Computer Science · Mathematics · #33C65 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 55N25 #Secondary 55N33

paper · pdf · doi:10.48550/arxiv.1804.00366

openalex publication_date 2018/04/02 · openalex created_date 2018/04/13 · openalex updated_date 2026/07/28

Abstract

We introduce relative twisted homology and cohomology groups associated with Euler type integrals of solutions to Lauricella's system F_D(a,b,c) of hypergeometric differential equations. We define an intersection form between relative twisted homology groups and that between relative twisted cohomology groups, and show their compatibility. We prove that the relative twisted homology group is canonically isomorphic to the space of local solutions to F_D(a,b,c) for any parameters a,b,c. Through this isomorphism, we study \cF_D(a,b,c) by the relative twisted homology and cohomology groups and the intersection forms without any conditions on a,b,c.

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