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}.
KANEV, V. (2004). Hurwitz spaces of triple coverings of elliptic curves and moduli spaces of Abelian threefolds. ANNALI DI MATEMATICA PURA ED APPLICATA, 183, 333-374 [10.1007/s10231-003-0098-9].
Hurwitz spaces of triple coverings of elliptic curves and moduli spaces of Abelian threefolds
KANEV, Vassil
2004-01-01
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}.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.