Mathematics > Algebraic Geometry
[Submitted on 29 Apr 2008 (v1), last revised 9 Apr 2015 (this version, v5)]
Title:The Kodaira dimension of the moduli space of Prym varieties
View PDFAbstract: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.
Submission history
From: Gavril Farkas [view email][v1] Tue, 29 Apr 2008 14:10:30 UTC (40 KB)
[v2] Wed, 28 May 2008 18:54:12 UTC (40 KB)
[v3] Tue, 23 Sep 2008 16:27:50 UTC (42 KB)
[v4] Mon, 17 Aug 2009 15:23:03 UTC (42 KB)
[v5] Thu, 9 Apr 2015 17:59:02 UTC (43 KB)
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