Shimura varieties in the Torelli locus via Galois coverings

2014/02/05 by Frediani, Paola, Ghigi, Alessandro, Penegini, Matteo · 3 citations
#14G35 #14H15 #14H40 #32G20 (primary) and 14K22 (secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1402.0973

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 in A_g. By a computer program we get the list of all families in genus up to 8 satisfying our condition. There is no family in genus 8, all of them are in genus at most 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 non-cyclic examples found by Moonen-Oort. We get 7 new non-abelian examples.

Cited by

• Families of cyclic curve coverings with maximal monodromy
• \mathbb Z_k^m-actions of signature (0;k,\stackreln+1…,k)
• Mumford-type Shimura curves contained in the Torelli locus

Related

• Shimura varieties in the Torelli locus via Galois coverings of elliptic curves
• On Shimura subvarieties generated by families of abelian covers of ℙ¹
• Infinitely many Shimura varieties in the Jacobian locus for g ≤ 4
• On Shimura curves generated by families of Galois G-covers of curves
• Shimura varieties and abelian covers of the line