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

2010/06/17 by B.J. Moonen, Moonen, Ben · 5 citations
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1006.3400

Abstract

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.

Cited by

• Families of cyclic curve coverings with maximal monodromy
• Mumford-type Shimura curves contained in the Torelli locus
• The Torelli locus and Newton polygons
• Positive density of primes of ordinary reduction for abelian varieties of simple signature
• Varieties with representable CH₀-group and a question of Colliot-Thélène

Related

• Shimura varieties and abelian covers of the line
• On cyclic covers of the projective line
• Shimura subvarieties in the Prym locus of ramified Galois coverings
• Families of Prym varieties of abelian coverings and Shimura varieties
• Shimura varieties in the Torelli locus via Galois coverings