Abstract
| Lingua originale | English |
|---|---|
| pagine (da-a) | 3006-3052 |
| Numero di pagine | 47 |
| Rivista | International Mathematics Research Notices |
| Volume | 2013 |
| Stato di pubblicazione | Published - 2013 |
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Unirationality of Hurwitz spaces of coverings of degree <= 5. / Kanev, Vassil.
In: International Mathematics Research Notices, Vol. 2013, 2013, pag. 3006-3052.Risultato della ricerca: Article
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TY - JOUR
T1 - Unirationality of Hurwitz spaces of coverings of degree <= 5
AU - Kanev, Vassil
PY - 2013
Y1 - 2013
N2 - Let Y be a smooth, projective curve of genus g>=1. Let H^0_{d,A}(Y)be the Hurwitz space which parametrizes coverings p:X --> Y of degree d simply branched in n=2e points, such that the monodromy group is S_d and det(P_*O_X/O_Y) is isomorphic to a fixed line bundle A^{-1} of degree e. We prove that when d=3, 4 or 5 and n is sufficiently large (precise bounds are given),these Hurwitz spaces are unirational. If in addition (e,2)=1 (when d=3), (e,6)=1 (when d=4) and (e,10)=1 (when d=5), then these Hurwitz spaces are rational.
AB - Let Y be a smooth, projective curve of genus g>=1. Let H^0_{d,A}(Y)be the Hurwitz space which parametrizes coverings p:X --> Y of degree d simply branched in n=2e points, such that the monodromy group is S_d and det(P_*O_X/O_Y) is isomorphic to a fixed line bundle A^{-1} of degree e. We prove that when d=3, 4 or 5 and n is sufficiently large (precise bounds are given),these Hurwitz spaces are unirational. If in addition (e,2)=1 (when d=3), (e,6)=1 (when d=4) and (e,10)=1 (when d=5), then these Hurwitz spaces are rational.
KW - Hurwitz spaces; unirationality; coverings; vector bundles.
UR - http://hdl.handle.net/10447/64970
UR - http://arxiv.org/abs/1106.1006
M3 - Article
VL - 2013
SP - 3006
EP - 3052
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
ER -