Enriques involutions on pencils of K3 surfaces

TL;DR

This paper classifies and explores Enriques involutions on three specific pencils of K3 surfaces with minimal discriminant, focusing on their coverage of Enriques surfaces.

Contribution

It provides a complete enumeration and analysis of Enriques surfaces covered by the general elements of Kondō's pencils I and II and the Apéry–Fermi pencil.

Findings

All Enriques surfaces covered by these pencils are identified.

The structure of Enriques involutions on these K3 surfaces is characterized.

Connections between the pencils and Enriques surfaces are clarified.

Abstract

The three pencils of K3 surfaces of minimal discriminant whose general element covers at least one Enriques surface are Kond\={o}'s pencils I and II, and the Ap\'ery--Fermi pencil. We enumerate and investigate all Enriques surfaces covered by their general elements.