Picard-Fuchs system for family of Kummer surfaces as subsystem of GKZ hypergeometric system
Atsuhira Nagano
TL;DR
This paper derives a simplified Picard-Fuchs system for a family of Kummer surfaces associated with principally polarized Abelian surfaces, using elliptic fibrations and GKZ hypergeometric systems.
Contribution
It provides a new explicit form of the Picard-Fuchs system for Kummer surfaces, connecting elliptic fibrations with GKZ hypergeometric systems.
Findings
Derived a rank five system of PDEs for Kummer surfaces
Connected elliptic fibrations with GKZ hypergeometric systems
Simplified the expression of the Picard-Fuchs system
Abstract
We determine a simple expression of the Picard-Fuchs system for a family of Kummer surfaces for all principally polarized Abelian surfaces. It is given by a system of linear partial differential equations in three variables of rank five. Our results are based on a Jacobian elliptic fibration on Kummer surfaces and a GKZ hypergeometric system suited to the elliptic fibration.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Computer Graphics and Visualization Techniques · Advanced Theoretical and Applied Studies in Material Sciences and Geometry