The Kodaira dimension of the moduli space of Prym varieties

Farkas, Gavril, and Ludwig, Katharina. "The Kodaira dimension of the moduli space of Prym varieties." Journal of the European Mathematical Society 012.3 (2010): 755-795. <http://eudml.org/doc/277480>.

@article{Farkas2010,
abstract = {We study the enumerative geometry of the moduli space $\mathcal \{R\}_g$ of Prym varieties of dimension $g-1$. Our main result is that the compactication of $\mathcal \{R\}_g$ 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 $\mathcal \{R\}_g$: 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. We also perform a detailed study of the singularities of the Prym moduli space, and show that for $g\ge 4$, pluricanonical forms extend to any desingularization of the moduli space.},
author = {Farkas, Gavril, Ludwig, Katharina},
journal = {Journal of the European Mathematical Society},
keywords = {Kodaira dimension; moduli space; Prym variety; Kodaira dimension; moduli space; Prym variety},
language = {eng},
number = {3},
pages = {755-795},
publisher = {European Mathematical Society Publishing House},
title = {The Kodaira dimension of the moduli space of Prym varieties},
url = {http://eudml.org/doc/277480},
volume = {012},
year = {2010},
}

TY - JOUR
AU - Farkas, Gavril
AU - Ludwig, Katharina
TI - The Kodaira dimension of the moduli space of Prym varieties
JO - Journal of the European Mathematical Society
PY - 2010
PB - European Mathematical Society Publishing House
VL - 012
IS - 3
SP - 755
EP - 795
AB - We study the enumerative geometry of the moduli space $\mathcal {R}_g$ of Prym varieties of dimension $g-1$. Our main result is that the compactication of $\mathcal {R}_g$ 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 $\mathcal {R}_g$: 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. We also perform a detailed study of the singularities of the Prym moduli space, and show that for $g\ge 4$, pluricanonical forms extend to any desingularization of the moduli space.
LA - eng
KW - Kodaira dimension; moduli space; Prym variety; Kodaira dimension; moduli space; Prym variety
UR - http://eudml.org/doc/277480
ER -