Fibred algebraic surfaces and commutators in the Symplectic group

[摘要] 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). (C) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-11-15

[关键词] Fibrations of algebraic surfaces;Number of singular fibres;Commutators;Mapping class group;Symplectic group;Symplectic fibrations;Stable fibrations