6533b833fe1ef96bd129b905
RESEARCH PRODUCT
On cubic elliptic varieties
Andrea Luigi TironiLuca UgagliaJuergen HausenAntonio Lafacesubject
Pure mathematicsMathematics::Commutative AlgebraGroup (mathematics)Applied MathematicsGeneral MathematicsFibrationMathematics - Algebraic GeometryHypersurfaceMathematics::Algebraic GeometryProjection (mathematics)Line (geometry)14C20 14DxxFOS: MathematicsMathematics (all)Finitely-generated abelian groupSettore MAT/03 - GeometriaCox ringAlgebraic Geometry (math.AG)Mathematicsdescription
Let X->P^(n-1) be an elliptic fibration obtained by resolving the indeterminacy of the projection of a cubic hypersurface Y of P^(n+1) from a line L not contained in Y. We prove that the Mordell-Weil group of the elliptic fibration is finite if and only if the Cox ring of X is finitely generated. We also provide a presentation of the Cox ring of X when it is finitely generated.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-05-14 |