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A global mirror symmetry framework for the Landau–Ginzburg/Calabi–Yau correspondence

Alessandro Chiodo, Yongbin Ruan (2011)

Annales de l’institut Fourier

We show how the Landau–Ginzburg/Calabi–Yau correspondence for the quintic three-fold can be cast into a global mirror symmetry framework. Then we draw inspiration from Berglund–Hübsch mirror duality construction to provide an analogue conjectural picture featuring all Calabi–Yau hypersurfaces within weighted projective spaces and certain quotients by finite abelian group actions.

A proof of the birationality of certain BHK-mirrors

Patrick Clarke (2014)

Complex Manifolds

We generalize and give an elementary proof of Kelly’s refinement [9] of Shoemaker’s result [11] on the birationality of certain BHK-mirrors. Our approach uses a construction that is equivalent to the Krawitz generalization [10] of the duality in Berglund-Hübsch [2].

Cyclic coverings of Fano threefolds

Sławomir Cynk (2003)

Annales Polonici Mathematici

We describe a series of Calabi-Yau manifolds which are cyclic coverings of a Fano 3-fold branched along a smooth divisor. For all the examples we compute the Euler characteristic and the Hodge numbers. All examples have small Picard number ϱ = h 1 , 1 .

Fourier Mukai transforms and applications to string theory.

Björn Andreas, Daniel Hernández Ruipérez (2005)


El artículo es una introducción a la transformación de Fourier-Mukai y sus aplicaciones a varios problemas de móduli, teoría de cuerdas y simetría "mirror". Se desarrollan los fundamentos necesarios para las transformaciones de Fourier-Mukai, entre ellos las categorías derivadas y los functores integrales. Se explican además sus versiones relativas, que se necesitan para precisar la noción de T-dualidad fibrada en variedades de Calabi-Yau elípticas de dimensión tres. Se consideran también varias...

Hodge numbers of a double octic with non-isolated singularities

Sławomir Cynk (2000)

Annales Polonici Mathematici

If B is a surface in ℙ³ of degree 8 which is the union of two smooth surfaces intersecting transversally then the double covering of ℙ³ branched along B has a non-singular model which is a Calabi-Yau manifold. The aim of this note is to compute the Hodge numbers of this manifold.

Homological projective duality

Alexander Kuznetsov (2007)

Publications Mathématiques de l'IHÉS

We introduce a notion of homological projective duality for smooth algebraic varieties in dual projective spaces, a homological extension of the classical projective duality. If algebraic varieties X and Y in dual projective spaces are homologically projectively dual, then we prove that the orthogonal linear sections of X and Y admit semiorthogonal decompositions with an equivalent nontrivial component. In particular, it follows that triangulated categories of singularities of these sections are...

Intrinsic pseudo-volume forms for logarithmic pairs

Thomas Dedieu (2010)

Bulletin de la Société Mathématique de France

We study an adaptation to the logarithmic case of the Kobayashi-Eisenman pseudo-volume form, or rather an adaptation of its variant defined by Claire Voisin, for which she replaces holomorphic maps by holomorphic K -correspondences. We define an intrinsic logarithmic pseudo-volume form Φ X , D for every pair ( X , D ) consisting of a complex manifold X and a normal crossing Weil divisor D on X , the positive part of which is reduced. We then prove that Φ X , D is generically non-degenerate when X is projective and K X + D ...

K3 fibrations on rigid double octic Calabi-Yau threefolds

Paweł Borówka (2016)

Annales Polonici Mathematici

We give a description of the Picard group of double octic Calabi-Yau threefolds using a K3 fibration defined by a singular line of the branch octic. In particular, we show that the group is generated by the Picard group of a generic fibre and the subgroup generated by the components of the reducible fibres.

Landau-Ginzburg models in real mirror symmetry

Johannes Walcher (2011)

Annales de l’institut Fourier

In recent years, mirror symmetry for open strings has exhibited some new connections between symplectic and enumerative geometry (A-model) and complex algebraic geometry (B-model) that in a sense lie between classical and homological mirror symmetry. I review the rôle played in this story by matrix factorizations and the Calabi-Yau/Landau-Ginzburg correspondence.

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