# The Kodaira dimension of the moduli space of Prym varieties

Gavril Farkas; Katharina Ludwig

Journal of the European Mathematical Society (2010)

- Volume: 012, Issue: 3, page 755-795
- ISSN: 1435-9855

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topFarkas, 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 -

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