Albanese varieties of abelian covers
Algebraic Geometry
2014-11-11 v2
Abstract
We show that Albanese varieties of abelian covers of projective plane are isogenous to product of isogeny components of abelian varieties associated with singularities of the ramification locus. In particular Albanese varieties of abelian covers of projective plane ramified over arrangements of lines and uniformized by unit ball are isogenous to a product of Jacobians of Fermat curves. Periodicity of the sequence of (semi-abelian) Albanese varieties of unramified cyclic covers of complements to a plane singular curve is shown.
Keywords
Cite
@article{arxiv.1401.5008,
title = {Albanese varieties of abelian covers},
author = {A. Libgober},
journal= {arXiv preprint arXiv:1401.5008},
year = {2014}
}
Comments
Substantial revision. Main changes in theorem 4.1 and sections 4 and 5. To appear in Journal of Singularities