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


Author: Jin-Xing Cai
Journal: Trans. Amer. Math. Soc. 358 (2006), 1187-1201
MSC (2000): Primary 14J50; Secondary 14J29
DOI: https://doi.org/10.1090/S0002-9947-05-03752-9
Published electronically: April 22, 2005
MathSciNet review: 2187650
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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 $\vert G\vert=2$, $K_S^2=4\chi (\mathcal O_S)$ and $q(S)=1$. Examples of such surfaces are given.


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Additional Information

Jin-Xing Cai
Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Email: cai@math.pku.edu.cn

DOI: https://doi.org/10.1090/S0002-9947-05-03752-9
Received by editor(s): October 31, 2003
Received by editor(s) in revised form: April 26, 2004
Published electronically: April 22, 2005
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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