Automorphisms of fiber surfaces of genus 2, inducing the identity in cohomology

Cai, Jin-Xing

doi:10.1090/S0002-9947-05-03752-9

Automorphisms of fiber surfaces of genus $2$, inducing the identity in cohomology
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Trans. Amer. Math. Soc. 358 (2006), 1187-1201 Request permission

Abstract:

Let $S$ be a complex non-singular projective surface of general type with a genus $2$ fibration and $\chi (\mathcal O_S)\geq 5$. Let $G \subset \operatorname {Aut}S$ be a non-trivial subgroup of automorphisms of $S$, inducing trivial actions on $H^i(S,\mathbb {Q})$ for all $i$. Then $|G|=2$, $K_S^2=4\chi (\mathcal O_S)$ and $q(S)=1$. Examples of such surfaces are given.

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