Surfaces of general type with q=2 are rigidified

Abstract

Let $S$ be a minimal smooth projective surface of general type with irregularity $q=2$. We show that, if $S$ 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 $q=2$ (which are not necessarily minimal) can be homotopic to the identity. In particular, such surfaces are rigidified in the sense of Fabrizio Catanese.

11 pages; Theorem 1.2 in the preliminary and Remark 3.2 are added; to appear in Communications in Contemporary Mathematics

References in corpus (3)

• Automorphism and Cohomology II: Complete intersections
• On the slope conjecture of Barja and Stoppino for fibred surfaces
• Automorphism and Cohomology I: Fano variety of lines and Cubic

Cited by in corpus (3)

• On topologically trivial automorphisms of compact Kähler manifolds and algebraic surfaces
• On numerically trivial automorphisms of threefolds of general type
• Automorphisms of 3-folds of general type acting trivially on cohomology