Lower Semi-Continuity of Entropy in a Family of K3 Surface Automorphisms

TL;DR

This paper investigates how the entropy of automorphisms on K3 surfaces varies with changes in the Picard rank, demonstrating lower semi-continuity in a broad family of such automorphisms.

Contribution

It extends the understanding of entropy behavior in K3 surface automorphisms by establishing lower semi-continuity across a large family, building on prior results by Xie.

Findings

Entropies vary in a lower semi-continuous manner with Picard rank changes.

The study covers a large class of K3 surface automorphisms in (P^1)^3.

Supports and extends previous theoretical results by Xie.

Abstract

We compute entropies in a large family of K3 surface automorphisms in (P^1)^3. In keeping with a result by Xie, we find that the entropies vary in a lower semi-continuous manner as the Picard ranks of the K3 surfaces vary.