Surfaces of general type with q = 2 are rigidified

Abstract

Let [Formula: see text] be a minimal smooth projective surface of general type with irregularity [Formula: see text]. We show that, if [Formula: see text] has a nontrivial holomorphic automorphism acting trivially on the cohomology with rational coefficients, then it is a surface isogenous to a product. As a consequence of this geometric characterization, one infers that no nontrivial automorphism of surfaces of general type with [Formula: see text] (which are not necessarily minimal) can be homotopic to the identity. In particular, such surfaces are rigidified in the sense of Fabrizio Catanese.