Automorphisms of surfaces of general type with q > 2 acting trivially in cohomology

摘要

In this paper we prove that surfaces of general type with irregularity q≥ 3 are rationally cohomologically rigidified, and so are minimal surfaces $S$ with q(S)= 2 unless K_S ~2 = 8χ(O _S. Here a surface S is said to be rationally cohomologically rigidified if its automorphism group Aut(S) acts faithfully on the cohomology ring H*(S?). As examples we give a complete classification of surfaces isogenous to a product with q(S)= 2 that are not rationally cohomologically rigidified.