# Enriques involutions on singular K3 surfaces of small discriminants

## TL;DR

This paper classifies Enriques involutions on singular K3 surfaces with small discriminants using lattice theory, and computes automorphism groups for some resulting Enriques surfaces, revealing their algebraic structures.

## Contribution

It provides a classification of Enriques involutions on singular K3 surfaces with small discriminants and applies Borcherds method to analyze their automorphism groups.

## Key findings

- Classification of Enriques involutions for discriminant ≤ 36
- Automorphism groups computed for 11 Enriques surfaces
- Detailed analysis of the most algebraic Enriques surfaces

## Abstract

We classify Enriques involutions on a K3 surface, up to conjugation in the automorphism group, in terms of lattice theory. We enumerate such involutions on singular K3 surfaces with transcendental lattice of discriminant smaller than or equal to 36. For 11 of these K3 surfaces, we apply Borcherds method to compute the automorphism group of the Enriques surfaces covered by them. In particular, we investigate the structure of the two most algebraic Enriques surfaces.