Hypergeometric Abelian Varieties

[摘要] In this paper, we construct abelian varieties associated to Gauss' and Appell--Lauricella hypergeometric series.Abelian varieties of this kind and the algebraic curves we defineto construct them were considered by several authors in settingsranging from monodromy groups (Deligne, Mostow), exceptional sets(Cohen, Wolfart, W"ustholz), modular embeddings (Cohen, Wolfart) toCM-type (Cohen, Shiga, Wolfart) and modularity (Darmon).Our contribution is to provide a complete, explicit and self-containedgeometric construction.

[学科分类] 数学（综合）