Geometry & Topology

Surface bundles over surfaces of small genus

Jim Bryan and Ron Donagi

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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
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
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

Subjects
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

Keywords
Surface bundles 4–manifolds algebraic surface

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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References

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