Infinitesimal deformations of rational surface automorphisms

Abstract

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 ).

Automorphism groups of rational surfaces

“…Indeed, under the condition (2), the most numerous automorphisms Bedford-Kim [1,2] and McMullen [10] constructed as realizations of Coxeter elements are those preserving cuspidal anticanonical curves. Note also that Grivaux showed that some of the automorphisms preserving cuspidal anticanonical curves are isolated in the sense that it is not possible to deform the pair (X, F ) of a surface X and an automorphism F : X → X (see [6], Theorem B). This is the reason why we consider the cuspidal anticanonical curves.…”