# A few explicit examples of complex dynamics of inertia groups on surfaces - a question of Professor Igor Dolgachev

## TL;DR

This paper provides explicit examples illustrating the complex dynamics of inertia groups associated with smooth rational curves on various types of surfaces, addressing an open question posed by Professor Igor Dolgachev.

## Contribution

It offers the first explicit examples of inertia group dynamics on surfaces, expanding understanding of their behavior on K3 and rational surfaces.

## Key findings

- Examples of inertia group dynamics on K3 surfaces
- Examples on rational surfaces and non-projective K3 surfaces
- Addresses an open question by Professor Dolgachev

## Abstract

We give a few explicit examples which answer an open minded question of Professor Igor Dolgachev on complex dynamics of the inertia group of a smooth rational curve on a projective K3 surface and its variants for a rational surface and a non-projective K3 surface.