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A bound on the dimension of a totally geodesic submanifold in the Prym locus

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Abstract

We give an upper bound for the dimension of a germ of a totally geodesic submanifold, and hence of a Shimura variety of \({{\mathcal {A}}}_{g-1}\), 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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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Milano, via Saldini 50, 20133, Milan, Italy

    Elisabetta Colombo

  2. Dipartimento di Matematica, Università di Pavia, via Ferrata 5, 27100, Pavia, Italy

    Paola Frediani

Authors
  1. Elisabetta Colombo
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  2. Paola Frediani
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Corresponding author

Correspondence to Elisabetta Colombo.

Additional information

The first author was partially supported by MIUR PRIN 2015 “Geometry of Algebraic Varieties”. The second author was partially supported by MIUR PRIN 2015 “Moduli spaces and Lie theory” and by FIRB 2012 “ Moduli Spaces and their Applications”. The authors were also partially supported by GNSAGA of INdAM.

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Colombo, E., Frediani, P. A bound on the dimension of a totally geodesic submanifold in the Prym locus. Collect. Math. 70, 51–57 (2019). https://doi.org/10.1007/s13348-018-0215-0

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  • DOI: https://doi.org/10.1007/s13348-018-0215-0

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