Complete subvarieties of moduli spaces and the Prym map
By Carel Faber, Gerard van der Geer. 2003
65 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2650b482f6c560ce5ce0b0d6465bdd14e18313a8
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In Geometry and Topology
- R. Pandharipande
- Carel Faber
- R. Pries
- Darren B. Glass
- Davesh Maulik
- A. Okounkov
- Richard P. Thomas
- Aaron Pixton
In Mathematical Physics
- R. Pandharipande
- Carel Faber
- R. Pries
- Darren B. Glass
- Davesh Maulik
- A. Okounkov
- Aaron Pixton
- Richard P. Thomas
Citations in the corpus
- Hodge integrals, partition matrices, and the λ g conjecture (2003, background): “This locus is complete in M g and of codimension g (see [ FvdG ]) — it may however”
- Hyperelliptic curves with prescribed p-torsion (2004, methodology): “For everyg and every 0≤ f ≤ g, the locusVg, f has codimensiong− f in M g, [1].”