6533b861fe1ef96bd12c5ae3
RESEARCH PRODUCT
Hurwitz spaces of quadruple coverings of elliptic curves and the moduli space of abelian threefolds A_3(1,1,4)
Vassil Kanevsubject
Pure mathematicsSubvarietyGeneral MathematicsCodimension14K10 (Primary) 14H10 14H30 (Secondary)Injective functionModuli spaceHurwitz spaces Abelian threefolds moduli unirationalityElliptic curveMathematics - Algebraic GeometryFOS: MathematicsAbelian groupAlgebraic Geometry (math.AG)Mathematicsdescription
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 space H_{4,n}(P^1) is unirational.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-01-01 |