Search results for "elliptic fibration"

showing 2 items of 2 documents

New fourfolds from F-theory

2015

In this paper, we apply Borcea-Voisin's construction and give new examples of fourfolds containing a del Pezzo surface of degree six, which admit an elliptic fibration on a smooth threefold. Some of these fourfolds are Calabi-Yau varieties, which are relevant for the $N=1$ compactification of Type IIB string theory known as $F$-Theory. As a by-product, we provide a new example of a Calabi--Yau threefold with Hodge numbers $h^{1,1}=h^{2,1}=10$.

14J50F-theory14J32del Pezzo surface14J32; 14J35; 14J50; Calabi-Yau manifolds; Del Pezzo surfaces; Elliptic fibration; F-theory; Mathematics (all)Calabi-Yau manifoldMathematics - Algebraic GeometryCalabi-Yau manifoldsFOS: MathematicsMathematics (all)14J35Settore MAT/03 - Geometriaelliptic fibrationDel Pezzo surfaces14J32 14J35 14J50Algebraic Geometry (math.AG)
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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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