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arXiv · 0804.4616

The Kodaira dimension of the moduli space of Prym varieties

Gavril Farkas·Katharina Ludwig
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Abstract

We study the enumerative geometry of the moduli space R_g of Prym varieties of dimension g-1 (also known as the space of admissible double covers). Our main result is that the compactification of R_g is of general type as soon as g>13. We achieve this by computing the class of two types of cycles on R_g: one defined in terms of Koszul cohomology of Prym curves, the other defined in terms of Raynaud theta divisors associated to certain vector bundles on curves. We formulate a Prym-Green conjecture on syzygies of Prym-canonical curves. In the appendix we show that even though R_g has non-canonical singularities, pluricanonical forms on R_g extend to any desingularization.

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Gavril Farkas, Katharina Ludwig. 2008-04-29. The Kodaira dimension of the moduli space of Prym varieties. https://arxiv.org/abs/0804.4616

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