Hurwitz spaces of triple coverings of elliptic curves and moduli spaces of abelian threefolds
Abstract
Description
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}.
43 pages, latex2e, some typos corrected, references updated, to appear in Annali di Matematica Pura ed Applicata
43 pages, latex2e, some typos corrected, references updated, to appear in Annali di Matematica Pura ed Applicata