0000000000795538

AUTHOR

Andrea Luigi Tironi

showing 2 related works from this author

On cubic elliptic varieties

2013

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.

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)Mathematics
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Del Pezzo elliptic varieties of degree d <= 4

2019

Let Y be a smooth del Pezzo variety of dimension n&gt;=3, i.e. a smooth complex projective variety endowed with an ample divisor H such that K_Y = (n+1)H. Let d be the degree H^n of Y and assume that d &gt;= 4. Consider a linear subsystem of |H| whose base locus is zero-dimensional of length d. The subsystem defines a rational map onto P^{n-1} and, under some mild extra hypothesis, the general pseudofibers are elliptic curves. We study the elliptic fibration X -&gt; P^{n-1} obtained by resolving the indeterminacy and call the variety X a del Pezzo elliptic variety. Extending the results of [7] we mainly prove that the Mordell-Weil group of the fibration is finite if and only if the Cox ring…

Pure mathematicsMathematics (miscellaneous)Elliptic fibrationSettore MAT/03 - GeometriaCox ringsDel Pezzo varietyTheoretical Computer ScienceDegree (temperature)Mathematics
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