Infinitesimal deformations of rational surface automorphisms

TL;DR

This paper investigates the infinitesimal deformations of rational surface automorphisms, focusing on the tangent space of the deformation space for pairs of surfaces and automorphisms, especially when the surface lacks holomorphic vector fields.

Contribution

It provides new insights into the local deformation theory of rational surface automorphisms, analyzing the Zariski tangent space in specific examples.

Findings

Identifies conditions under which the tangent space is trivial or nontrivial.

Provides explicit computations for certain classes of rational surfaces.

Enhances understanding of the deformation behavior of automorphisms on rational surfaces.

Abstract

If $X$ is a rational surface without nonzero holomorphic vector field and $f$ is an automorphism of $X$, we study in several examples the Zariski tangent space of the local deformation space of the pair $(X, f)$.