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Characteristic varieties of algebraic curves
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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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From Regions to Hodge Structures: The Topological Study of semialgebraic Curves Configurations
The node contribution psi determines region counts and deletion-restriction for ordinary curve arrangements, equals dim Gr_4^W H^2 for line arrangements, and the simplified OS defect is sum binom(k_x-1,2) over nodes w...
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