6533b856fe1ef96bd12b305a

RESEARCH PRODUCT

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

Vassil KanevVassil Kanev

subject

Pure mathematicsTrace (linear algebra)Degree (graph theory)Hurwitz spaces Abelian threefolds Prym varieties moduli unirationalityApplied MathematicsHolomorphic functionSpace (mathematics)Moduli spaceElliptic curveMathematics - Algebraic GeometryMathematics::Algebraic GeometrySimple (abstract algebra)14K10 (Primary) 14H30 14D07 (Secondary)FOS: MathematicsAbelian groupAlgebraic Geometry (math.AG)Mathematics

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}.

yearjournalcountryeditionlanguage
2002-07-31
10.1007/s10231-003-0098-9http://arxiv.org/abs/math/0207305