Search results for "14J35"

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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Big Vector Bundles on Surfaces and Fourfolds

2019

The aim of this note is to exhibit explicit sufficient criteria ensuring bigness of globally generated, rank-$r$ vector bundles, $r \geqslant 2$, on smooth, projective varieties of even dimension $d \leqslant 4$. We also discuss connections of our general criteria to some recent results of other authors, as well as applications to tangent bundles of Fano varieties, to suitable Lazarsfeld-Mukai bundles on four-folds, etcetera.

Pure mathematicsbig vector bundles Lazarsfeld-MukaipositivityGeneral Mathematics010102 general mathematicsDimension (graph theory)Vector bundleTangentFano planevector bundles01 natural sciences14J60 (Primary) 14J35 (Secondary)010101 applied mathematicsMathematics - Algebraic Geometryvector bundles; positivity; vanishing criteriaMathematics::Algebraic Geometryvanishing criteriaFOS: MathematicsSettore MAT/03 - Geometria0101 mathematicsAlgebraic Geometry (math.AG)Mathematics::Symplectic GeometryMathematics
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