Shimura subvarieties via endomorphisms

Spelta, Irene

Comptes Rendus. Mathématique, Tome 360 (2022) no. G10, pp. 1117-1124.

We prove that there exist two families in ${ℳ}_2,{ℳ}_3$ of non-Galois covers of the projective line whose Jacobians trace out Shimura subvarieties of ${𝒜}_2,{𝒜}_3$. They provide the first two explicit examples of Shimura subvarieties obtained by means of Jacobians carrying non-trivial endomorphisms not directly induced by the automorphisms of the curves. We also obtain a new example of a positive dimensional family of special Pryms in ${𝒜}_4^{\delta }$.

Classification : 14H10, 14H30, 14H40, 14G35

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