Skip to main content
Passa alla visualizzazione normale.

VASSIL KANEV

Unirationality of Hurwitz spaces of coverings of degree <= 5

  • Authors: Kanev, V
  • Publication year: 2013
  • Type: Articolo in rivista (Articolo in rivista)
  • Key words: Hurwitz spaces; unirationality; coverings; vector bundles.
  • OA Link: http://hdl.handle.net/10447/64970

Abstract

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.