Geometry & Topology 6 (2002) 59–67

DOI: 10.2140/gt.2002.6.59

arXiv: math.AG/0105203

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.

Keywords

Surface bundles, 4–manifolds, algebraic surface

Mathematical Subject Classification

Primary: 14D05, 14D06, 57M20

Secondary: 14J29, 57N05, 57N13

References

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Publication

Received: 24 May 2001
Revised: 7 February 2002
Accepted: 26 February 2002
Published: 27 February 2002
Proposed: Dieter Kotschick
Seconded: Walter Neumann, Gang Tian

Authors