Equivariant Gromov - Witten Invariants

Abstract

We develop general theory of equivariant quantum cohomology for ample Kahler manifolds and prove the mirror conjecture for projective complete intersections.

48 pages, LaTeX v 2.09

References in corpus (3)

• On Quantum Cohomology Rings for Hypersurfaces in $C{P}^{N-1}$
• On equivariant quantum cohomology
• Stacks of Stable Maps and Gromov-Witten Invariants

Cited by in corpus (52)

• Integrating Over Higgs Branches
• Quantum integrability and supersymmetric vacua
• Branes and N=2 Theories in Two Dimensions
• Quantum Cohomology and Virasoro Algebra
• Computing Genus-Zero Twisted Gromov-Witten Invariants
• Landau-Ginzburg/Calabi-Yau correspondence for quintic three-folds via symplectic transformations
• Instanton sums and five-dimensional gauge theories
• BPS/CFT correspondence IV: sigma models and defects in gauge theory
• The Abelian/Nonabelian Correspondence and Frobenius Manifolds
• Quantum periods - I. Semi-infinite variations of Hodge structures
• Vortex partition functions, wall crossing and equivariant Gromov-Witten invariants
• Quantum D-modules and generalized mirror transformations
• The Crepant Transformation Conjecture for Toric Complete Intersections
• Generalized periods and mirror symmetry in dimensions n>3
• Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds
• Crepant resolutions and open strings
• Reconstruction and Convergence in Quantum $K$-Theory via Difference Equations
• J-holomorphic curves, moment maps, and invariants of Hamiltonian group actions
• A lecture on Arithmetic Mirror Symmetry and Calabi-Yau manifolds
• On the Structure of the Small Quantum Cohomology Rings of Projective Hypersurfaces
• The Eynard-Orantin recursion and equivariant mirror symmetry for the projective line
• The Stringy Instanton Partition Function
• Mirror Principle II
• Dual Pairs of Gauged Linear Sigma Models and Derived Equivalences of Calabi-Yau threefolds
• Stable maps to Looijenga pairs
• Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories
• On Quantum Cohomology Rings for Hypersurfaces in $C{P}^{N-1}$
• Seidel elements and mirror transformations
• Painleve' transcendents and two-dimensional topological field theory
• Relative quasimaps and mirror formulae
• Towards a quantum Lefschetz hyperplane theorem in all genera
• Gromov-Witten invariants and localization
• A Landau-Ginzburg model for Lagrangian Grassmannians, Langlands duality and relations in quantum cohomology
• Crepant resolution and the holomorphic anomaly equation for C^3/Z_3
• Mirror pairs of Calabi-Yau threefolds from mirror pairs of quasi-Fano threefolds
• A Mirror Theorem for the Mirror Quintic
• Local B-model Yukawa couplings from A-twisted correlators
• Wall-Crossing in Genus Zero Landau-Ginzburg Theory
• Mathematical results inspired by physics
• The Period map for quantum cohomology of ${\mathbb{P}}^2$
• Open Virtual Structure Constants and Mirror Computation of Open Gromov-Witten Invariants of Projective Hypersurfaces
• Motivic integration and the birational invariance of BCOV invariants
• Laurent polynomials in Mirror Symmetry: why and how?
• Hori's Equation for Gravitational Virtual Structure Constants of Calabi-Yau Hypersurface in CP^{N-1}
• Versality in mirror symmetry
• Localization computation of one-point disk invariants of projective Calabi-Yau complete intersections
• Les Houches lectures on non-perturbative Seiberg-Witten geometry
• The Genus One Gromov-Witten Invariants of Calabi-Yau Complete Intersections
• A reconstruction of Euler data
• On the semi-simplicity of the quantum cohomology algebras of complete intersections
• Stringy Instanton Counting and Topological Strings
• The fundamental solution matrix and relative stable maps