Surface bundles over surfaces of small genus

Details Surface bundles over surfaces of small genus Surface bundles over surfaces of small genus

2001-05-24

arxiv.org/abs/math/0105203v2

Geom. Topol. 6 (2002) 59-67

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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