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, exhibiting several examples and in particular 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,Z).
Fibred algebraic surfaces and commutators in the Symplectic group
Zannier U.
2020
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, exhibiting several examples and in particular 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,Z).File in questo prodotto:
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