On K3 surfaces which dominate Kummer surfaces

TL;DR

This paper investigates the relationships between K3 surfaces and Kummer surfaces, establishing new Torelli-type and Kummer sandwich theorems that deepen understanding of their isogeny relations.

Contribution

It introduces a Torelli-type theorem for rational maps from K3 to Kummer surfaces and a Kummer sandwich theorem for K3 surfaces with Shioda-Inose structures.

Findings

Proved a Torelli-type theorem for rational maps.

Established a Kummer sandwich theorem.

Enhanced understanding of isogeny relations between K3 and Kummer surfaces.

Abstract

We study isogeny relations between K3 surfaces and Kummer surfaces. Specifically, we prove a Torelli-type theorem for the existence of rational maps from K3 surfaces to Kummer surfaces, and a Kummer sandwich theorem for K3 surfaces with Shioda-Inose structure.