# Coble's question and complex dynamics of inertia groups on surfaces

## TL;DR

This paper investigates the inertia groups of rational curves on K3 surfaces using topological entropy, addressing a long-standing question about the inertia group of a generic Coble surface.

## Contribution

It provides new insights into the structure of inertia groups on K3 surfaces and applies topological entropy to study their dynamics, solving an open problem posed by Coble.

## Key findings

- Characterization of inertia groups on 2-elementary and singular K3 surfaces
- Application of topological entropy to understand inertia group dynamics
- Resolution of Coble's open question on generic Coble surfaces

## Abstract

We study the inertia groups of some smooth rational curves on 2-elementary K3 surfaces and singular K3 surfaces from the view of topological entropy, with an application to a long standing open question of Coble on the inertia group of a generic Coble surface.