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

Vassil Kanev

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 th…