Automorphism groups of certain Enriques surfaces

TL;DR

This paper computes the automorphism groups of specific Enriques surfaces, including n-nodal and cuspidal types, and describes their actions on rational curves and elliptic fibrations.

Contribution

It provides explicit calculations of automorphism groups for certain Enriques surfaces and details their actions on geometric structures, advancing understanding of their symmetries.

Findings

Automorphism groups of n-nodal Enriques surfaces are explicitly determined.

Automorphism groups of cuspidal Enriques surfaces are characterized.

The action of automorphisms on rational curves and elliptic fibrations is described.

Abstract

We calculate the automorphism group of certain Enriques surfaces. The Enriques surfaces that we investigate include very general $n$-nodal Enriques surfaces and very general cuspidal Enriques surfaces. We also describe the action of the automorphism group on the set of smooth rational curves and on the set of elliptic fibrations.