Symmetric spaces uniformizing Shimura varieties in the Torelli locus
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Publication:6352184
DOI10.1007/S10231-022-01193-YarXiv2010.13159MaRDI QIDQ6352184
Publication date: 25 October 2020
Abstract: An algebraic subvariety Z of A_g is totally geodesic if it is the image via the natural projection map of some totally geodesic submanifold X of the Siegel space. We say that X is the symmetric space uniformizing Z. In this paper we determine which symmetric space uniformizes each of the low genus counterexamples to the Coleman-Oort conjecture obtained studying Galois covers of curves. It is known that the counterexamples obtained via Galois covers of elliptic curves admit two fibrations in totally geodesic subvarieties. The second result of the paper studies the relationship between these fibrations and the uniformizing symmetric space of the examples.
Jacobians, Prym varieties (14H40) Modular and Shimura varieties (14G35) Families, moduli of curves (analytic) (14H15)
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