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- Title
Shimura Varieties in the Torelli Locus via Galois Coverings.
- Authors
Frediani, Paola; Ghigi, Alessandro; Penegini, Matteo
- Abstract
Given a family of Galois coverings of the projective line, we give a simple sufficient condition ensuring that the closure of the image of the family via the period mapping is a special (or Shimura) subvariety of Ag. By a computer program we get the list of all families in genus g≤ 9 satisfying our condition. There are no families with g= 8, 9; all of them are in genus g≤ 7. These examples are related to a conjecture of Oort. Among them we get the cyclic examples constructed by various authors (Shimura, Mostow, De Jong-Noot, Rohde, Moonen, and others) and the abelian noncyclic examples found by Moonen-Oort. We get seven new nonabelian examples.
- Subjects
SHIMURA varieties; GALOIS modules (Algebra); ARITHMETICAL algebraic geometry; COMPACT Abelian groups; NONABELIAN groups
- Publication
IMRN: International Mathematics Research Notices, 2015, Vol 2015, Issue 20, p10595
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnu272