Surface bundles over surfaces of small genus

Abstract

We construct examples of non-isotrivial algebraic families of smooth complex projective curves over a curve of genus 2. This solves a problem from Kirby's list of problems in low-dimensional topology. Namely, we show that 2 is the smallest possible base genus that can occur in a 4-manifold of non-zero signature which is an oriented fiber bundle over a Riemann surface. A refined version of the problem asks for the minimal base genus for fixed signature and fiber genus. Our constructions also provide new (asymptotic) upper bounds for these numbers.

Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper3.abs.html

References in corpus (3)

• Lefschetz fibrations and the Hodge bundle
• Commutators, Lefschetz fibrations and the signatures of surface bundles
• Diffeomorphisms, symplectic forms, and Kodaira fibrations

Cited by in corpus (11)

• Supermoduli Space Is Not Projected
• Sections of surface bundles
• The arithmeticity of a Kodaira Fibration is determined by its universal cover
• Double Kodaira fibrations
• On Kodaira fibrations with invariant cohomology
• Signatures of surface bundles and stable commutator lengths of Dehn twists
• Extra-special quotients of surface braid groups and double Kodaira fibrations with small signature
• Indecomposable surface bundles over surfaces
• Complex surfaces with mutually non-biholomorphic universal covers
• Surface bundles over surfaces: new inequalities between signature, simplicial volume and Euler characteristic
• Nonisotrivial families over curves with fixed point free automorphisms