A survey of Calabi-Yau manifolds

2008/01/01 by Shing–Tung Yau · 1 citation
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory

paper · pdf · doi:10.4310/sdg.2008.v13.n1.a9

openalex publication_date 2008/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

Homological mirror symmetry 299 7. SYZ geometric interpretation of mirror symmetry 300 7.1. Special Lagrangian submanifolds in Calabi-Yau manifolds 300 7.2. The SYZ conjecture -SYZ transformation 301 7.3. Special Lagrangian geometry 301 7.4. Special Lagrangian fibrations 302 7.5. The SYZ transformation 303 7.6. The SYZ conjecture and tropical geometry 303 8. Geometries related to Calabi-Yau manifolds 304 8.

Citations

• Mirror Symmetry For Zeta Functions
• Euler number of the compactified Jacobian and multiplicity of rational curves
• The number of plane conics 5-fold tangent to a given curve
• The Self-Duality Equations on a Riemann Surface
• Special Lagrangian Fibrations I: Topology
• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Scalar Curvature and Projective Embeddings, I
• Arithmetic and Attractors
• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
• Vector Bundles over Elliptic Fibrations
• On the work of Givental relative to mirror symmetry
• Framed knots at large N
• Some numerical results in complex differential geometry
• Ring-Theoretic Properties of Certain Hecke Algebras
• Compact k�hler manifolds of positive bisectional curvature
• A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory
• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
• Vector Bundles Over an Elliptic Curve
• Noether-Lefschetz theory and the Yau-Zaslow conjecture
• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• REFLEXIVE POLYHEDRA, WEIGHTS AND TORIC CALABI-YAU FIBRATIONS
• Modular Elliptic Curves and Fermat's Last Theorem
• Equivariant Gromov - Witten Invariants
• Enumerative tropical algebraic geometry in R2
• Counting Elliptic Curves in K3 Surfaces
• The Reduced Genus-One Gromov-Witten Invariants of Calabi-Yau Hypersurfaces
• Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds
• Complete K�hler manifolds with zero Ricci curvature II
• Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds
• Calibrated geometries
• Mirror Maps, Modular Relations and Hypergeometric Series I
• M-Theory and Topological Strings--II

Cited by

• Calabi–Yau manifold [wikipedia]