Complete subvarieties of moduli spaces and the Prym map
Algebraic Geometry
2007-05-23 v2
Abstract
We prove that in characteristic p>0 the locus of stable curves of p-rank at most f is pure of codimension g-f in the moduli space of stable curves. Then we consider the Prym map and analyze it using tautological classes. We study the locus of curves with an etale double cover of p-rank 0 in some detail. In particular, in genus 2 we obtain a formula for the number of such curves. We end with several examples illustrating our formula.
Cite
@article{arxiv.math/0305334,
title = {Complete subvarieties of moduli spaces and the Prym map},
author = {Carel Faber and Gerard van der Geer},
journal= {arXiv preprint arXiv:math/0305334},
year = {2007}
}
Comments
20 pages, 1 figure. Final version, to appear in J. Reine Angew. Math