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arXiv · 1505.03929

Surfaces of general type with q=2 are rigidified

Wenfei Liu
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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.

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Wenfei Liu. 2017-12-06. Surfaces of general type with q=2 are rigidified. https://doi.org/10.1142/s0219199717500845

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