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The Oort conjecture on Shimura curves in the Torelli locus of hyperelliptic curves

Kang ZuoXin Lu

subject

Shimura varietyPure mathematicsConjectureMathematics::Number TheoryApplied MathematicsGeneral Mathematics010102 general mathematics05 social sciencesComplex multiplicationMathematics::Geometric Topology01 natural sciencesTorelli theoremAlgebraMathematics::Algebraic Geometry0502 economics and business0101 mathematicsLocus (mathematics)050203 business & managementMathematics

description

Abstract Oort has conjectured that there do not exist Shimura varieties of dimension >0 contained generically in the Torelli locus of genus-g curves when g is sufficiently large. In this paper we prove the analogue of this conjecture for Shimura curves with respect to the hyperelliptic Torelli locus of genus g > 7 .

yearjournalcountryeditionlanguage
2017-10-01Journal de Mathématiques Pures et Appliquées
https://doi.org/10.1016/j.matpur.2017.05.002