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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 primitiveExpand
Almost toric symplectic four-manifolds
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 spaceExpand
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 deformedExpand
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 FourierExpand
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
Geometric structures on G2 and Spin (7)-manifolds
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 andExpand
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 curvesExpand
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
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 haveExpand