Geodesic
Surface bundles over surfaces of small genus
Bryan, Jim1 ; Donagi, Ron2
1 Department of Mathematics, University of British Columbia, 121-1984 Mathematics Road, Vancouver, V6T 1Z2, British Columbia, Canada
2
Geometry & topology, Tome 6 (2002) no. 1, pp. 59-67.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/gt.2002.6.59
Keywords: Surface bundles, 4–manifolds, algebraic surface

Bryan, Jim 1 ; Donagi, Ron 2

1 Department of Mathematics, University of British Columbia, 121-1984 Mathematics Road, Vancouver, V6T 1Z2, British Columbia, Canada
2 
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Bryan, Jim; Donagi, Ron. Surface bundles over surfaces of small genus. Geometry & topology, Tome 6 (2002) no. 1, pp. 59-67. doi : 10.2140/gt.2002.6.59. http://geodesic.mathdoc.fr/articles/10.2140/gt.2002.6.59/

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