53 citations · 434 across the 46 of their papers we have counts for
22 papers · 1 filter
A Note on Disk Counting in Toric Orbifolds
Kwokwai Chan, Cheol-Hyun Cho, Siu-Cheong Lau +2
We compute orbi-disk invariants of compact Gorenstein semi-Fano toric orbifolds by extending the method used for toric Calabi-Yau orbifolds. As a consequence the orbi-disc potentia…
Pseudotoric structures and special Lagrangian torus fibrations on certain flag varieties
Kwokwai Chan, Naichung Conan Leung, Changzheng Li
We construct pseudotoric structures (à la Tyurin) on the two-step flag variety , and explain a general relation between pseudotoric structures and special Lagran…
Geometric quantization via SYZ transforms
Kwokwai Chan, Yat-Hin Suen
The so-called quantization problem in geometric quantization is asking whether the space of wave functions is independent of the choice of polarization. In this paper, we apply SYZ…
Quasimap SYZ for toric Calabi-Yau manifolds
Kwokwai Chan
In this note, we study the SYZ mirror construction for a toric Calabi-Yau manifold using instanton corrections coming from Woodward's quasimap Floer theory instead of Fukaya-Oh-Oht…
Homological mirror symmetry for local Calabi-Yau manifolds via SYZ
Kwokwai Chan
This is a write-up of the author's talk in the conference "Algebraic Geometry in East Asia 2016" held at the University of Tokyo in January 2016. We give a survey on a series of pa…
Lagrangian sections on mirrors of toric Calabi-Yau 3-folds
Kwokwai Chan, Daniel Pomerleano, Kazushi Ueda
We construct Lagrangian sections of a Lagrangian torus fibration on a 3-dimensional conic bundle, which are SYZ dual to holomorphic line bundles over the mirror toric Calabi-Yau 3-…
SYZ mirror symmetry for toric varieties
Kwokwai Chan
We survey recent developments in the study of SYZ mirror symmetry for compact toric and toric Calabi-Yau varieties, with a special emphasis on works of the author and his collabora…
Gross fibrations, SYZ mirror symmetry, and open Gromov-Witten invariants for toric Calabi-Yau orbifolds
Kwokwai Chan, Cheol-Hyun Cho, Siu-Cheong Lau +1
For a toric Calabi-Yau (CY) orbifold whose underlying toric variety is semi-projective, we construct and study a non-toric Lagrangian torus fibration on …
Lagrangian torus fibrations and homological mirror symmetry for the conifold
Kwokwai Chan, Daniel Pomerleano, Kazushi Ueda
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
Kwokwai Chan, Kazushi Ueda
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 wi…
Open Gromov-Witten invariants, mirror maps, and Seidel representations for toric manifolds
Kwokwai Chan, Siu-Cheong Lau, Naichung Conan Leung +1
Let be a compact toric Kähler manifold with nef. Let be a regular fiber of the moment map of the Hamiltonian torus action on . Fukaya-Oh-Ohta-Ono defined…
Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds
Kwokwai Chan, Cheol-Hyun Cho, Siu-Cheong Lau +1
We investigate the relationship between the Lagrangian Floer superpotentials for a toric orbifold and its toric crepant resolutions. More specifically, we study an open string vers…
Homological mirror symmetry for -resolutions as a -duality
Kwokwai Chan
We study Homological Mirror Symmetry (HMS) for -resolutions from the SYZ viewpoint. Let $X\to\bC^2/\bZ_{n+1}$ be the crepant resolution of the -singularity. The mirror of…
Open Gromov-Witten invariants and mirror maps for semi-Fano toric manifolds
Kwokwai Chan, Siu-Cheong Lau, Naichung Conan Leung +1
We prove that for a compact toric manifold whose anti-canonical divisor is numerically effective, the Lagrangian Floer superpotential defined by Fukaya-Oh-Ohto-Ono is equal to the…
Enumerative meaning of mirror maps for toric Calabi-Yau manifolds
Kwokwai Chan, Siu-Cheong Lau, Hsian-Hua Tseng
We prove that the inverse of a mirror map for a toric Calabi-Yau manifold of the form , where is a compact toric Fano manifold, can be expressed in terms of generating fun…
Matrix factorizations from SYZ transformations
Kwokwai Chan, Naichung Conan Leung
It is known that Lagrangian torus fibers of the moment map of a toric Fano manifold , equipped with flat -connections, are mirror to matrix factorizations of the mirror su…
SYZ mirror symmetry for toric Calabi-Yau manifolds
Kwokwai Chan, Siu-Cheong Lau, Naichung Conan Leung
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 Ca…
A formula equating open and closed Gromov-Witten invariants and its applications to mirror symmetry
Kwokwai Chan
We prove that open Gromov-Witten invariants for semi-Fano toric manifolds of the form , where is a toric Fano manifold, are equal to certa…
The Ooguri-Vafa metric, holomorphic discs and wall-crossing
Kwokwai Chan
Recently, Gaiotto, Moore and Neitzke \cite{GMN08} proposed a new construction of hyperkähler metrics. In particular, they gave a new construction of the Ooguri-Vafa metric, in whic…
Holomorphic line bundles on projective toric manifolds from Lagrangian sections of their mirrors by SYZ transformations
Kwokwai Chan
The mirror of a projective toric manifold is given by a Landau-Ginzburg model . We introduce a class of Lagrangian submanifolds in and show that, under the SYZ…
On SYZ mirror transformations
Kwokwai Chan, Naichung Conan Leung
In this expository paper, we discuss how Fourier-Mukai-type transformations, which we call SYZ mirror transformations, can be applied to provide a geometric understanding of the mi…
Mirror symmetry for toric Fano manifolds via SYZ transformations
Kwokwai Chan, Naichung Conan Leung
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.