Skip to main content
Passa alla visualizzazione normale.

VASSIL KANEV

Hurwitz spaces of triple coverings of elliptic curves and moduli spaces of Abelian threefolds

  • Authors: KANEV, V
  • Publication year: 2004
  • Type: Articolo in rivista
  • Key words: Hurwitz spaces, Abelian threefolds, Prym varieties, moduli, unirationality
  • OA Link: http://hdl.handle.net/10447/18522

Abstract

We prove that the moduli spaces A_3(D) of polarized abelian threefolds with polarizations of types D=(1,1,2), (1,2,2), (1,1,3) or (1,3,3) are unirational. The result is based on the study of families of simple coverings of elliptic curves of degree 2 or 3 and on the study of the corresponding period mappings associated with holomorphic differentials with trace 0. In particular we prove the unirationality of the Hurwitz space H_{3,A}(Y) which parameterizes simply branched triple coverings of an elliptic curve Y with determinants of the Tschirnhausen modules isomorphic to A^{-1}.