Kummer surfaces associated to (1,2)-polarized abelian surfaces

TL;DR

This paper explores the geometric structure of a specific class of Kummer surfaces linked to (1,2)-polarized abelian surfaces, revealing their relation to del Pezzo surfaces and elliptic fibrations with particular singular fibers.

Contribution

It provides a detailed description of the geometry of Kummer surfaces associated with (1,2)-polarized abelian surfaces, including their double cover structure and elliptic fibration properties.

Findings

Kummer surface is a double cover of a weak del Pezzo surface.

The surface inherits an elliptic fibration with twelve I_2 singular fibers.

The geometric structure relates to specific polarization types on abelian surfaces.

Abstract

The aim of this paper is to describe the geometry of the generic Kummer surface associated to a $(1,2)$-polarized abelian surface. We show that it is the double cover of a weak del Pezzo surface and that it inherits from the del Pezzo surface an elliptic fibration with twelve singular fibers of type $I_2.$