Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry
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In this article, a new higher dimensional version of the McKay correspondence is proposed, which enables us to understand the "Hodge numbers" assigned to singular Gorenstein varieties by physicists, leading to the conjecture that string theory indicates the existence of some new cohomology theory H st ∗ (X) for algebraic varieties with gird singularities.About:
This article is published in Topology.The article was published on 1996-10-01 and is currently open access. It has received 259 citations till now. The article focuses on the topics: Mirror symmetry & String theory.read more
Citations
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A New Cohomology Theory of Orbifold
TL;DR: In this paper, a new cohomology ring for almost complex orbifolds is constructed based on the string theory model in physics, and the key theorem is the associativity of this new ring.
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Germs of arcs on singular algebraic varieties and motivic integration
Jan Denef,François Loeser +1 more
TL;DR: In this paper, the authors studied the rationality of the Poincare series associated to p-adic points on a singular algebraic variety and its images under truncations, and proved a rationality result for these points.
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Orbifold Gromov-Witten Theory
Weimin Chen Chen,Yongbin Ruan +1 more
TL;DR: In this paper, the notion of good map was introduced and used to establish Gromov-Witten theory for orbifolds, and the good map theory was used to define good map.
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On Calabi-Yau Complete Intersections in Toric Varieties
Victor V. Batyrev,Lev A. Borisov +1 more
TL;DR: In this article, it was shown that the combinatorial duality proposed by second author agrees with the duality for Hodge numbers predicted by mirror symmetry, and that the complete verification of mirror symmetry predictions for singular Calabi-Yau varieties of arbitrary dimension requires considerations of string-theoretic Hodge number.
References
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Book
Introduction to Toric Varieties.
TL;DR: In this article, a mini-course is presented to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications, concluding with Stanley's theorem characterizing the number of simplicies in each dimension in a convex simplicial polytope.
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Strings on orbifolds
TL;DR: In this article, the authors considered string propagation on the quotient of a flat torus by a discrete group and obtained an exactly soluble and more or less realistic method of string compactification.
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Théorie de Hodge : III
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Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties
TL;DR: In this article, it was shown that there exists an isomorphism between two conformal field theories corresponding to Calabi-Yau varieties from two families of algebraic compactifications of affine hypersurfaces.
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The geometry of toric varieties
TL;DR: Affine toric varieties have been studied in this article, where the definition of an affine Toric variety and its properties have been discussed, including cones, lattices, and semigroups.