Data di Pubblicazione:
2020
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.
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.
Tipologia CRIS:
4.1 Contributo in Atti di convegno
Keywords:
Second fundamental form, Prym map, totally geodesic submanifold.
Elenco autori:
Colombo, Elisabetta; Frediani, Paola
Link alla scheda completa:
Titolo del libro:
Galois Covers, Grothendieck-Teichmueller Theory and Dessins d'Enfants - Interactions between Geometry, Topology, Number Theory and Algebra
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