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Surface bundles over
surfaces of small genus
Jim Bryan and Ron Donagi |
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Geometry & Topology 6 (2002) 59–67
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DOI: 10.2140/gt.2002.6.59
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arXiv: math.AG/0105203 |
Abstract |
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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
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Mathematical Subject Classification 2000
Primary: 14D05, 14D06, 57M20
Secondary: 57N05, 57N13, 14J29
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References |
Forward citations |
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
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Authors |
| Jim Bryan | |
| Department of Mathematics University of British Columbia 121-1984 Mathematics Road Vancouver V6T 1Z2 British Columbia Canada |
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| Ron Donagi | |
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