%0 Journal Article
%T The Kodaira dimension of the moduli space of Prym varieties
%A Gavril Farkas
%A Katharina Ludwig
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0804.4616v5