Characteristic varieties of algebraic curves

Details Characteristic varieties of algebraic curves Characteristic varieties of algebraic curves

1998-01-13

arxiv.org/abs/math/9801070v2

Mathematics

Algebraic Geometry

50p. Expanded version. To appear in Proceedings of NATO workshop on applications of algebraic Geometry, Elsevier

Scientific paper

We study tori attached to the fundamental groups of plane curves with arbitrary singularities. These tori provide complete information about homology of finite abelian covers of the plane branched along the curve. We calculate these tori in terms of certain linear systems determined by the singularities of the curve. In the case of the complements to a union of lines they can be calculated from the lattice of the arrangement and are closely related to the components of the space of Aomoto complexes with prescribed homology.

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