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The Kodaira dimension of the moduli space of Prym varieties

Gavril Farkas; Katharina Ludwig — 2010

Journal of the European Mathematical Society

We study the enumerative geometry of the moduli space $ℛ_{g}$ of Prym varieties of dimension $g - 1$ . Our main result is that the compactication of $ℛ_{g}$ is of general type as soon as $g > 13$ and $g$ is different from 15. 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....

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