Surface bundles over surfaces of small genus
Algebraic Geometry
2014-11-11 v2 Geometric Topology
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.
Cite
@article{arxiv.math/0105203,
title = {Surface bundles over surfaces of small genus},
author = {Jim Bryan and Ron Donagi},
journal= {arXiv preprint arXiv:math/0105203},
year = {2014}
}
Comments
Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper3.abs.html