Quantum cohomology and toric minimal model programs

DOI10.1016/j.aim.2019.07.004zbMath1440.14252arXiv1207.3253OpenAlexW2964676916MaRDI QIDQ2319885

Eduardo González, Christopher T. Woodward

Publication date: 20 August 2019

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.3253

zbMATH Keywords

toric varietiesquantum cohomology

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Geometric invariant theory (14L24) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Quantization in field theory; cohomological methods (81T70) Minimal model program (Mori theory, extremal rays) (14E30)

Related Items (13)

A mirror construction for the big equivariant quantum cohomology of toric manifolds ⋮ Global mirrors and discrepant transformations for toric Deligne-Mumford stacks ⋮ Compactness in the adiabatic limit of disk vortices ⋮ Open-closed Gromov-Witten invariants of 3-dimensional Calabi-Yau smooth toric DM stacks ⋮ Floer cohomology and flips ⋮ Quantum Kirwan morphism and Gromov-Witten invariants of quotients. III ⋮ A wall-crossing formula for Gromov-Witten invariants under variation of git quotient ⋮ A Leray-Serre spectral sequence for Lagrangian Floer theory ⋮ Lagrange multiplier functionals and their applications in symplectic geometry and string topology ⋮ Gamma classes and quantum cohomology ⋮ Local model for moduli space of affine vortices ⋮ On exceptional collections of line bundles and mirror symmetry for toric Del-Pezzo surfaces ⋮ Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Seidel elements and mirror transformations
• Quantum Kirwan morphism and Gromov-Witten invariants of quotients. II
• Groupe de Picard des variétés de modules de fibrés semi-stable sur les courbes algébriques. (Picard groups of moduli varieties of semi- stable bundles on algebraic curves)
• The quantum orbifold cohomology of weighted projective spaces
• Lagrangian Floer theory on compact toric manifolds. II: Bulk deformations
• Gauged Floer theory of toric moment fibers
• An integral structure in quantum cohomology and mirror symmetry for toric orbifolds
• Quantum Kirwan morphism and Gromov-Witten invariants of quotients. III
• Derived categories of toric varieties
• Quantum \(D\)-modules and generalized mirror transformations
• Polyedres de Newton et nombres de Milnor
• Localization of virtual classes
• Variation of geometric invariant theory quotients. (With an appendix: ``An example of a thick wall by Nicolas Ressayre)
• Quantum cohomology via \(D\)-modules
• Symplectic cuts
• Open Gromov-Witten invariants and mirror maps for semi-Fano toric manifolds
• On the quantum homology algebra of toric Fano manifolds
• Hodge-theoretic mirror symmetry for toric stacks
• Quantum Kirwan morphism and Gromov-Witten invariants of quotients. I
• Properness for scaled gauged maps
• Displacing Lagrangian toric fibers by extended probes
• Éléments de géométrie algébrique. III: Étude cohomologique des faisceaux cohérents. (Séconde partie). Rédigé avec la colloboration de J. Dieudonné
• Lagrangian Floer theory on compact toric manifolds. I.
• Lagrangian Floer theory and mirror symmetry on compact toric manifolds
• Gromov–Witten Invariants of Toric Fibrations
• Chow ring of projective nonsingular torus embedding
• The orbifold Chow ring of toric Deligne-Mumford stacks
• Topological properties of Hamiltonian circle actions
• A mirror theorem for toric stacks
• Gromov-Witten theory of Deligne-Mumford stacks
• Angular momentum, convex Polyhedra and Algebraic Geometry
• THE GEOMETRY OF TORIC VARIETIES
• A mirror theorem for toric complete intersections
• Quantum Cohomology Rings of Toric Manifolds
• The Gromov-Witten invariants of symplectic toric manifolds, and their quantum cohomology ring
• Quasimap Floer Cohomology for Varying Symplectic Quotients
• Equivariant Gromov - Witten Invariants
• Convergence of quantum cohomology by quantum Lefschetz
• Orbifold quantum cohomology of weighted projective spaces
• Geometric invariant theory and flips
• Introduction to the Mori program

This page was built for publication: Quantum cohomology and toric minimal model programs