An integral structure in quantum cohomology and mirror symmetry for toric orbifolds
Hiroshi Iritani,Hiroshi Iritani +1 more
TLDR
In this article, an integral structure in orbifold quantum cohomology associated to the K-group and the Γ ˆ-class was introduced. But the integral structure was not shown to match with the natural integral structure for the Landau-Ginzburg model under mirror symmetry.About:
This article is published in Advances in Mathematics.The article was published on 2009-10-20 and is currently open access. It has received 296 citations till now. The article focuses on the topics: Crepant resolution & Cohomology ring.read more
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Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary
Kentaro Hori,Mauricio Romo +1 more
TL;DR: In this paper, the authors compute the partition function on the hemisphere of a class of twodimensional (2,2) supersymmetric field theories including gauged linear sigma models and provide a general exact formula for the central charge of the D-brane placed at the boundary.
OtherDOI
Lectures on K-theoretic computations in enumerative geometry
TL;DR: In this paper, the main conjecture of arXiv:hep-th/0412021 and the conjectures of ar Xiv:1404.2323 in the simplest case of reduced smooth curves were proved.
Journal ArticleDOI
Gamma classes and quantum cohomology of Fano manifolds: Gamma conjectures
TL;DR: Gamma conjectures for Fano manifolds have been proposed in this paper, which can be thought of as a square root of the index theorem, and they can be seen as a refinement of Dubrovin's Gamma conjecture II.
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Wall-crossing in genus zero quasimap theory and mirror maps
TL;DR: In this article, a geometric interpretation of the mirror map as a generating series of quasimap invariants is presented, and wall-crossing formulas for all targets W==G which admit a torus action with isolated xed points are proved for zero loci of sections of homogeneous vector bundles on such targets.
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Landau–Ginzburg/Calabi–Yau correspondence for quintic three-folds via symplectic transformations
TL;DR: In this paper, the authors show that the Fan-Jarvis-Ruan-Witten theory of W-curves in genus zero for quintic polynomials in five variables can be computed via a symplectic transformation.
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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Mirror symmetry is T duality
TL;DR: In this paper, it was argued that every Calabi-Yau manifold X with a mirror Y admits a family of supersymmetric toroidal 3-cycles and that the moduli space of such cycles together with their flat connections is precisely the space Y.
Book
Mirror Symmetry
Eric Zaslow,Ravi Vakil,Kentaro Hori,Richard P. Thomas,Cumrun Vafa,Albrecht Klemm,Rahul Pandharipande,Sheldon Katz +7 more
TL;DR: In this paper, the authors proved mirror symmetry for supersymmetric sigma models on Calabi-Yau manifolds in 1+1 dimensions and showed that the equivalence of the gauged linear sigma model embedded in a theory with an enlarged gauge symmetry, with a Landau-Ginzburg theory of Toda type Standard R -> 1/R duality and dynamical generation of superpotential by vortices.
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The moment map and equivariant cohomology
TL;DR: In this article, the authors propose a solution to solve the problem of spamming, which is called spamming-based spamming.$$$/$/$/$/$$