Automorphismes naturels de l'espace de Douady de points sur une surface

TL;DR

This paper investigates the automorphism group of the Douady space of points on a surface, analyzing how surface automorphisms influence it and exploring their cohomological actions and fixed point classifications.

Contribution

It provides new insights into the size and structure of automorphism groups of Douady spaces and characterizes automorphisms induced by surface automorphisms.

Findings

Automorphisms from surface automorphisms act on cohomology.

Classification of fixed points of these automorphisms.

Results on the size of the automorphism group of the Douady space.

Abstract

We prove some general results concerning the size of the group of automorphisms of the Douady space of points on a surface. We then study some properties of the automorphisms coming from an automorphism of the surface, in particular their action on the cohomology and the classification of their fixed points.