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Branes and toric geometry

We show that toric geometry can be used rather effectively to translate a brane configuration to geometry. Roughly speaking the skeletons of toric space are identified with the brane configurations.… Expand

The enumerative geometry of K3 surfaces and modular forms

We prove the conjectures of Yau-Zaslow and Gottsche concerning the number curves on K3 surfaces. Specifically, let X be a K3 surface and C be a holomorphic curve in X representing a primitive… Expand

Almost toric symplectic four-manifolds

- N. Leung, Margaret Symington
- Mathematics
- 8 December 2003

Almost toric manifolds form a class of singular Lagrangian fibered symplectic manifolds that is a natural generalization of toric manifolds. Notable examples include the K3 surface, the phase space… Expand

From special Lagrangian to Hermitian–Yang–Mills via Fourier–Mukai transform

We exhibit a transformation taking special Lagrangian submanifolds of a Calabi-Yau together with local systems to vector bundles over the mirror manifold with connections obeying deformed… Expand

Mirror Symmetry Without Corrections

- N. Leung
- Mathematics, Physics
- 27 September 2000

We give geometric explanations and proofs of various mirror symmetry conjectures for T -invariant Calabi-Yau manifolds when instanton corrections are absent. This uses a fiberwise Fourier… Expand

SYZ mirror symmetry for toric Calabi-Yau manifolds

- Kwokwai Chan, Siu-Cheong Lau, N. Leung
- Mathematics, Physics
- 19 June 2010

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 manifold… Expand

Geometric structures on G2 and Spin (7)-manifolds

- Jae-Hyouk Lee, N. Leung
- Mathematics, Physics
- 6 February 2002

This article studies the geometry of moduli spaces of G2-manifolds, associative cycles, coassociative cycles and deformed Donaldson-Thomas bundles. We introduce natural symmetric cubic tensors and… Expand

Generating functions for the number of curves on abelian surfaces

Let X be an Abelian surface and C a holomorphic curve in X representing a primitive homology class. The space of genus g curves in the class of C is g dimensional. We count the number of such curves… Expand

Geometry of the Maurer-Cartan equation near degenerate Calabi-Yau varieties

- Kwokwai Chan, N. Leung, Z. Ma
- Mathematics
- 28 February 2019

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 of… Expand

Topological quantum field theory for Calabi-Yau threefolds and G-2 manifolds

- N. Leung
- Mathematics, Physics
- 15 August 2002

We introduce a homology theory whose Euler characteristics counts ASD bundles over four dimensional co-associative submanifolds in (almost) G_2 manifolds.
As a TQFT, in relative situations, we have… Expand

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