Finite symmetry groups in complex geometry

TL;DR

This paper explores finite symmetry groups in complex geometry, discussing methods like equivariant minimal models and recent classification results for K3-surfaces with specific symmetries, aimed at a broad mathematical audience.

Contribution

It provides an accessible overview of symmetry groups in complex geometry and introduces recent classification work on K3-surfaces with particular symmetries.

Findings

Classification of K3-surfaces with special symmetry

Development of equivariant minimal model program for surfaces

Broad exposition suitable for a wide audience

Abstract

On June 5, 2007 the second author delivered a talk at the Journees de l'Institut Elie Cartan entitled "Finite symmetry groups in complex geometry". This paper begins with an expanded version of that talk which, in the spirit of the Journees, is intended for a wide audience. The later paragraphs are devoted both to the exposition of basic methods, in particular an equivariant minimal model program for surfaces, as well as an outline of recent work of the authors on the classification of K3-surfaces with special symmetry.