Search results for " Abelian threefolds"

showing 2 items of 2 documents

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

2002

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}.

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
researchProduct

Hurwitz spaces of quadruple coverings of elliptic curves and the moduli space of abelian threefolds A_3(1,1,4)

2005

We prove that the moduli space A_3(1,1,4) of polarized abelian threefolds with polarization of type (1,1,4) is unirational. By a result of Birkenhake and Lange this implies the unirationality of the isomorphic moduli space A_3(1,4,4). The result is based on the study the Hurwitz space H_{4,n}(Y) of quadruple coverings of an elliptic curve Y simply branched in n points. We prove the unirationality of its codimension one subvariety H^{0}_{4,A}(Y) which parametrizes quadruple coverings ��:X --> Y with Tschirnhausen modules isomorphic to A^{-1}, where A\in Pic^{n/2}Y, and for which ��^*:J(Y)--> J(X) is injective. This is an analog of the result of Arbarello and Cornalba that the Hurwitz s…

Pure mathematicsSubvarietyGeneral MathematicsCodimension14K10 (Primary) 14H10 14H30 (Secondary)Injective functionModuli spaceHurwitz spaces Abelian threefolds moduli unirationalityElliptic curveMathematics - Algebraic GeometryFOS: MathematicsAbelian groupAlgebraic Geometry (math.AG)Mathematics
researchProduct