Note on a Geometric Isogeny of K3 Surfaces

TL;DR

This paper explores a geometric two-isogeny between two classes of K3 surfaces, linking lattice-polarized surfaces with those arising from double covers of the projective plane branched over six lines.

Contribution

It establishes a new correspondence demonstrating a geometric two-isogeny between specific lattice-polarized K3 surfaces and those from double covers of the plane.

Findings

Identifies a geometric two-isogeny between the two classes of K3 surfaces.

Provides a correspondence relating lattice-polarized K3 surfaces to double covers.

Enhances understanding of the geometric relationships among K3 surfaces.

Abstract

The paper establishes a correspondence relating two specific classes of complex algebraic K3 surfaces. The first class consists of K3 surfaces polarized by the rank-sixteen lattice H+E_7+E_7. The second class consists of K3 surfaces obtained as minimal resolutions of double covers of the projective plane branched over a configuration of six lines. The correspondence underlies a geometric two-isogeny of K3 surfaces.