Unirationality of Hurwitz spaces of coverings of degree <= 5

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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 ofdegree 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.
Lingua originaleEnglish
pagine (da-a)3006-3052
Numero di pagine47
RivistaInternational Mathematics Research Notices
Stato di pubblicazionePublished - 2013

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