Albanese varieties of abelian covers

Journal of Singularities
volume 12 (2015), 105-123

Received 1 May 2014. Received in revised form 20 August 2014.

DOI: 10.5427/jsing.2015.12g

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Abstract:

We show that the Albanese variety of an abelian cover of the projective plane is isogenous to a product of isogeny components of abelian varieties associated with singularities of the ramification locus provided certain conditions are met. In particular Albanese varieties of abelian covers of P^2 ramified over arrangements of lines and uniformized by the unit ball in C62 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.

Author(s) information:

Anatoly Libgober