Classification of fiber surfaces of genus 2 with automorphisms acting trivially in cohomology

Jin-Xing Cai

Vol. 232 (2007), No. 1, 43–59

DOI: 10.2140/pjm.2007.232.43

Abstract

Let S be a complex nonsingular projective surface of general type with a fibration of genus 2, and let G ⊂ Aut S be a nontrivial subgroup of automorphisms of S, inducing trivial actions on H²(S, ℚ). We give a classification for pairs (S,G) from the point of view of moduli. Consequently, we show that there exist surfaces S of general type (with p_g arbitrary large) with an involution acting trivially on Hⁱ(S, ℤ) for all i.

Keywords

surfaces of general type, automorphism groups, fibrations

Mathematical Subject Classification 2000

Primary: 14J50

Secondary: 14J29

Milestones

Received: 5 April 2006

Revised: 1 February 2007

Accepted: 19 February 2007

Published: 1 September 2007