Complete subvarieties of moduli spaces and the Prym map

Details Complete subvarieties of moduli spaces and the Prym map Complete subvarieties of moduli spaces and the Prym map

2003-05-23

arxiv.org/abs/math/0305334v2

Mathematics

Algebraic Geometry

20 pages, 1 figure. Final version, to appear in J. Reine Angew. Math

Scientific paper

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.

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