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.
Kanev, V. (2013). Unirationality of Hurwitz spaces of coverings of degree <= 5. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2013(13), 3006-3052.
Data di pubblicazione: | 2013 |
Titolo: | Unirationality of Hurwitz spaces of coverings of degree <= 5 |
Autori: | |
Citazione: | Kanev, V. (2013). Unirationality of Hurwitz spaces of coverings of degree <= 5. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2013(13), 3006-3052. |
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Digital Object Identifier (DOI): | http://dx.doi.org/10.1093/imrn/rns138 |
URL: | http://arxiv.org/abs/1106.1006 |
Settore Scientifico Disciplinare: | Settore MAT/03 - Geometria |
Appare nelle tipologie: | 1.01 Articolo in rivista |
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