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SYZ mirror symmetry for toric Calabi-Yau manifolds
We investigate mirror symmetry for toric Calabi-Yau manifolds from the perspective of the SYZ conjecture. Starting with a non-toric special Lagrangian torus fibration on a toric Calabi-Yau manifoldExpand
Geometry of the Maurer-Cartan equation near degenerate Calabi-Yau varieties
Given a degenerate Calabi-Yau variety X equipped with local deformation data, we construct an almost differential graded Batalin-Vilkovisky (almost dgBV) algebra PV(X), giving a singular version ofExpand
Homological mirror symmetry for An-resolutions as a T-duality
  • Kwokwai Chan
  • Mathematics, Computer Science
  • J. Lond. Math. Soc.
  • 5 December 2011
TLDR
A geometric functor is constructed from a derived Fukaya category of $\check{X}$ to the derived category of coherent sheaves on $X$ and it is shown that this is an equivalence of triangulation categories onto a full triangulated subcategory of $D^b(X)$, thus realizing Kontsevich's HMS conjecture by SYZ. Expand
Open Gromov-Witten invariants and superpotentials for semi-Fano toric surfaces
In this paper, we compute the open Gromov-Witten invariants for every compact toric surface X which is semi-Fano (i.e. the anticanonical line bundle is nef). Unlike the Fano case, this involvesExpand
Lagrangian Torus Fibrations and Homological Mirror Symmetry for the Conifold
We discuss homological mirror symmetry for the conifold from the point of view of the Strominger–Yau–Zaslow conjecture.
Dual torus fibrations and homological mirror symmetry for $A_n$-singularities
We study homological mirror symmetry for not necessarily compactly supported coherent sheaves on the minimal resolutions of A_n-singularities. An emphasis is put on the relation with theExpand
Scattering diagrams from asymptotic analysis on Maurer–Cartan equations
We investigate SYZ mirror symmetry via asymptotic analysis on Maurer-Cartan equations, following a program set forth by Fukaya. Let $X_0$ and $\check{X}_0$ be a mirror pair of semi-flat Calabi-YauExpand
Gross fibrations, SYZ mirror symmetry, and open Gromov–Witten invariants for toric Calabi–Yau orbifolds
Given a toric Calabi-Yau orbifold X whose underlying toric variety is semi- projective, we construct and study a non-toric Lagrangian torus bration on X , which we call the Gross bration. We applyExpand
Mirror symmetry for toric Fano manifolds via SYZ transformations
Abstract We construct and apply Strominger–Yau–Zaslow mirror transformations to understand the geometry of the mirror symmetry between toric Fano manifolds and Landau–Ginzburg models.
The Ooguri-Vafa metric, holomorphic discs and wall-crossing
Recently, Gaiotto, Moore and Neitzke \cite{GMN08} proposed a new construction of hyperk\"{a}hler metrics. In particular, they gave a new construction of the Ooguri-Vafa metric, in which they cameExpand
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