Gap theorems and achirality for automorphisms of K3 surfaces and Enriques surfaces

TL;DR

This paper establishes gap theorems for entropy norms on automorphism groups of K3 and Enriques surfaces and investigates the achirality of their automorphisms through genus-one fibrations.

Contribution

It introduces new gap theorems for entropy norms and analyzes achirality conditions for automorphisms of K3 and Enriques surfaces.

Findings

Proved gap theorems for entropy norms on automorphism groups.

Studied achirality of automorphisms via genus-one fibrations.

Extended results to irreducible holomorphic symplectic manifolds.

Abstract

We prove gap theorems for entropy norms on automorphism groups of K3 surfaces, Enriques surfaces, and irreducible holomorphic symplectic manifolds. We also study the achirality of automorphisms of K3 surfaces and Enriques surfaces in terms of genus-one fibrations.