In this paper we study the second fundamental form of the Prym map in the ramified case. 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, contained in the Prym locus.
Second Fundamental Form of the Prym Map in the Ramified Case / E. Colombo, P. Frediani (SPRINGER PROCEEDINGS IN MATHEMATICS & STATISTICS). - In: Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants / [a cura di] F. Neumann,S. Schroll. - [s.l] : Springer, 2020. - ISBN 9783030517946. - pp. 55-66 (( Interactions between Geometry, Topology, Number Theory and Algebra Leicester 2018 [10.1007/978-3-030-51795-3_4].
Second Fundamental Form of the Prym Map in the Ramified Case
E. Colombo;
2020
Abstract
In this paper we study the second fundamental form of the Prym map in the ramified case. 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, contained in the Prym locus.
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