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

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}.

arXiv comment43 pages, latex2e, some typos corrected, references updated, to appear in Annali di Matematica Pura ed Applicata

References in corpus (3)

• Vector Bundles over Elliptic Fibrations
• A note on Hurwitz schemes of covers of a positive genus curve
• An Isomorphism Between Moduli Spaces of Abelian Varieties

Cited by in corpus (6)

• Generic Torelli theorem for Prym varieties of ramified coverings
• Hurwitz spaces of Galois coverings of P^1 with Galois groups Weyl groups
• Hurwitz spaces of quadruple coverings of elliptic curves and the moduli space of abelian threefolds A_3(1,1,4)
• Unirationality of Hurwitz spaces of coverings of degree <= 5
• Polarization types of isogenous Prym-Tyurin varieties
• Hurwitz moduli varieties parameterizing Galois covers of an algebraic curve