## Geometry & Topology

### 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.

#### Article information

Source
Geom. Topol., Volume 6, Number 1 (2002), 59-67.

Dates
Revised: 7 February 2002
Accepted: 26 February 2002
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.gt/1513882789

Digital Object Identifier
doi:10.2140/gt.2002.6.59

Mathematical Reviews number (MathSciNet)
MR1885589

Zentralblatt MATH identifier
1038.57006

#### Citation

Bryan, Jim; Donagi, Ron. Surface bundles over surfaces of small genus. Geom. Topol. 6 (2002), no. 1, 59--67. doi:10.2140/gt.2002.6.59. https://projecteuclid.org/euclid.gt/1513882789

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