Geometry & Topology
- Geom. Topol.
- Volume 6, Number 1 (2002), 59-67.
Surface bundles over surfaces of small genus
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.
Geom. Topol., Volume 6, Number 1 (2002), 59-67.
Received: 24 May 2001
Revised: 7 February 2002
Accepted: 26 February 2002
First available in Project Euclid: 21 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.) 14D06: Fibrations, degenerations 57M20: Two-dimensional complexes
Secondary: 57N05: Topology of $E^2$ , 2-manifolds 57N13: Topology of $E^4$ , $4$-manifolds [See also 14Jxx, 32Jxx] 14J29: Surfaces of general type
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