Automorphisms of surfaces of general type with q=1 acting trivially in cohomology

Abstract

Let S be a complex minimal surface of general type with irregularity q(S)=1 and Aut_0(S) the subgroup of automorphisms acting trivially on the cohomology ring with rational coefficients. In this paper we show that |Aut_0(S)|<=4, and if the equality holds then $S$ is a surface isogenous to a product of unmixed type. Moreover, examples of surfaces with |Aut_0(S)|=4 and all possible values of the geometric genus are provided.

37 pages; a proof of the Lefschetz fixed point theorem is added; the appendix is expanded a little bit; to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci

References in corpus (2)

• Automorphisms of surfaces of general type with q=1 acting trivially in cohomology
• Surfaces of general type with q=2 are rigidified

Cited by in corpus (4)

• Automorphisms of surfaces of general type with q=1 acting trivially in cohomology
• 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