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arXiv · 1906.05806

Fibred algebraic surfaces and commutators in the Symplectic group

Fabrizio Catanese·Pietro Corvaja·Umberto Zannier
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Abstract

We describe the minimal number of critical points and the minimal number $s$ of singular fibres for a non isotrivial fibration of a surface $S$ over a curve $B$ of genus $1$, constructing a fibration with $s=1$ and irreducible singular fibre with $4$ nodes. Then we consider the associated factorizations in the mapping class group and in the symplectic group. We describe explicitly which products of transvections on homologically independent and disjoint circles are a commutator in the Symplectic group $Sp (2g, \mathbb{Z})$.

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Fabrizio Catanese, Pietro Corvaja, Umberto Zannier. 2019-06-13. Fibred algebraic surfaces and commutators in the Symplectic group. https://arxiv.org/abs/1906.05806

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