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arXiv:math/0207305 [math.AG]AbstractReferencesReviewsResources

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

Vassil Kanev

Published 2002-07-31, updated 2003-08-03Version 3

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}.

Comments: 43 pages, latex2e, some typos corrected, references updated, to appear in Annali di Matematica Pura ed Applicata
Journal: Ann. Mat. Pura Appl. (4) Vol. 183 (2004), pp. 333 - 374.
Categories: math.AG
Subjects: 14K10, 14H30, 14D07
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