Search results for "Del Pezzo surface"

showing 3 items of 3 documents

Lines on the Dwork pencil of quintic threefolds

2012

We present an explicit parametrization of the families of lines of the Dwork pencil of quintic threefolds. This gives rise to isomorphic curves which parametrize the lines. These curves are 125:1 covers of certain genus six curves. These genus six curves are first presented as curves in P^1*P^1 that have three nodes. It is natural to blow up P^1*P^1 in the three points corresponding to the nodes in order to produce smooth curves. The result of blowing up P^1*P^1 in three points is the quintic del Pezzo surface dP_5, whose automorphism group is the permutation group S_5, which is also a symmetry of the pair of genus six curves. The subgroup A_5, of even permutations, is an automorphism of ea…

High Energy Physics - TheoryConifoldDel Pezzo surfaceGeneral MathematicsFOS: Physical sciencesGeneral Physics and AstronomyParity of a permutationGeometryPermutation groupAutomorphismQuintic functionBlowing upCombinatoricsMathematics - Algebraic GeometryMathematics::Algebraic GeometryHigh Energy Physics - Theory (hep-th)FOS: MathematicsAlgebraic Geometry (math.AG)Pencil (mathematics)MathematicsAdvances in Theoretical and Mathematical Physics
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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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Enumerative Aspects of the Gross-Siebert Program

2015

For the last decade, Mark Gross and Bernd Siebert have worked with a number of collaborators to push forward a program whose aim is an understanding of mirror symmetry. In this chapter, we’ll present certain elements of the “Gross-Siebert” program. We begin by sketching its main themes and goals. Next, we review the basic definitions and results of two main tools of the program, logarithmic and tropical geometry. These tools are then used to give tropical interpretations of certain enumerative invariants. We study in detail the tropical pencil of elliptic curves in a toric del Pezzo surface. We move on to a basic illustration of mirror symmetry, Gross’s tropical construction for \(\mathbb{P…

AlgebraElliptic curvePure mathematicsDel Pezzo surfaceLogarithmTropical geometryQAMirror symmetryMathematics::Symplectic GeometryPhysics::Atmospheric and Oceanic PhysicsPencil (mathematics)MathematicsEnumerative geometry
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