The wall-crossing formula and Lagrangian mutations

DOI10.1016/j.aim.2019.106850zbMath1433.53107arXiv1711.03209OpenAlexW2995495021WikidataQ126563463 ScholiaQ126563463MaRDI QIDQ2288070

James Pascaleff, Dmitry Tonkonog

Publication date: 17 January 2020

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

Full work available at URL: https://arxiv.org/abs/1711.03209

zbMATH Keywords

cluster transformationmutationLagrangian torusLandau-Ginzburg potentialwall-crossingholomorphic disk

Mathematics Subject Classification ID

Symplectic and contact topology in high or arbitrary dimension (57R17) Fano varieties (14J45) Lagrangian submanifolds; Maslov index (53D12) Symplectic aspects of Floer homology and cohomology (53D40) Mirror symmetry (algebro-geometric aspects) (14J33)

Related Items (10)

Mirror symmetry for truncated cluster varieties ⋮ An-type surface singularity and nondisplaceable Lagrangian tori ⋮ Exotic Lagrangian tori in Grassmannians ⋮ Immersed two-spheres and SYZ with application to Grassmannians ⋮ Tropical Lagrangians in toric del-Pezzo surfaces ⋮ SYZ mirror symmetry for hypertoric varieties ⋮ Families of monotone Lagrangians in Brieskorn-Pham hypersurfaces ⋮ From symplectic cohomology to Lagrangian enumerative geometry ⋮ Refined disk potentials for immersed Lagrangian surfaces ⋮ Disk counting and wall-crossing phenomenon via family Floer theory

Cites Work

• Unnamed Item
• Unnamed Item
• Minkowski polynomials and mutations
• Upper bounds for mutations of potentials
• On exotic Lagrangian tori in \(\mathbb{CP}^{2}\)
• On the Fukaya category of a Fano hypersurface in projective space
• Compactness for holomorphic curves with switching Lagrangian boundary conditions
• An open string analogue of Viterbo functoriality
• Fukaya categories and Picard-Lefschetz theory
• Floer cohomology and disc instantons of Lagrangian torus fibers in Fano toric manifolds
• Symplectic submanifolds and almost-complex geometry
• From symplectic cohomology to Lagrangian enumerative geometry
• Infinitely many monotone Lagrangian tori in del Pezzo surfaces
• Floer trajectories and stabilizing divisors
• Products of Floer cohomology of torus fibers in toric Fano manifolds
• Homological mirror symmetry for Calabi-Yau hypersurfaces in projective space
• Cluster algebras I: Foundations
• Infinitely many exotic monotone Lagrangian tori in ℂℙ²
• Landau-Ginzburg models -- old and new
• Displacing Lagrangian toric fibers via probes
• Birational geometry of cluster algebras
• A biased view of symplectic cohomology
• Rigid subsets of symplectic manifolds
• Special Lagrangian fibrations, wall-crossing, and mirror symmetry
• Graded lagrangian submanifolds
• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Symplectic hypersurfaces in the complement of an isotropic submanifold
• Lectures on symplectic geometry

This page was built for publication: The wall-crossing formula and Lagrangian mutations