We give an upper bound for the dimension of a germ of a totally geodesic submanifold, and hence of a Shimura variety of Ag−1 , contained in the Prym locus. First we give such a bound for a germ passing through a Prym variety of a k-gonal curve in terms of the gonality k. Then we deduce a bound only depending on the genus g.
A bound on the dimension of a totally geodesic submanifold in the Prym locus / E. Colombo, F. Paola. - In: COLLECTANEA MATHEMATICA. - ISSN 0010-0757. - 70:1(2019 Jan), pp. 51-57. [10.1007/s13348-018-0215-0]
A bound on the dimension of a totally geodesic submanifold in the Prym locus
E. Colombo
;
2019
Abstract
We give an upper bound for the dimension of a germ of a totally geodesic submanifold, and hence of a Shimura variety of Ag−1 , contained in the Prym locus. First we give such a bound for a germ passing through a Prym variety of a k-gonal curve in terms of the gonality k. Then we deduce a bound only depending on the genus g.
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