In this paper we study the second fundamental form of the Prym map Pg,r : R_{g,r} → A^δ_{g−1+r} in the ramified case r > 0. We give an expression of it in terms of the second fundamental form of the Torelli map of the covering curves. We use this expression to give an upper bound for the dimension of a germ of a totally geodesic submanifold, and hence of a Shimura subvariety of A^δ_{g−1+r} , contained in the Prym locus.
Second fundamental form of the Prym map in the ramified case
Paola Frediani
2020-01-01
Abstract
In this paper we study the second fundamental form of the Prym map Pg,r : R_{g,r} → A^δ_{g−1+r} in the ramified case r > 0. We give an expression of it in terms of the second fundamental form of the Torelli map of the covering curves. We use this expression to give an upper bound for the dimension of a germ of a totally geodesic submanifold, and hence of a Shimura subvariety of A^δ_{g−1+r} , contained in the Prym locus.File in questo prodotto:
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