Special subvarieties arising from families of cyclic covers of the projective line

Details Special subvarieties arising from families of cyclic covers of the projective line Special subvarieties arising from families of cyclic covers of the projective line

2010-06-17

arxiv.org/abs/1006.3400v2

Mathematics

Algebraic Geometry

Minor improvements. To appear in Documenta Math

Scientific paper

We consider families of cyclic covers of the projective line, where we fix
the covering group and the local monodromies and we vary the branch points. We
prove that there are precisely twenty such families that give rise to a special
subvariety in the moduli space of abelian varieties. Our proof uses techniques
in mixed characteristics due to Dwork and Ogus.

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