Toric degenerations of integrable systems on Grassmannians and polygon spaces

DOI10.1215/00277630-2643839zbMath1304.37037arXiv1111.4809OpenAlexW3098681358MaRDI QIDQ5169720

Yuichi Nohara, Kazushi Ueda

Publication date: 11 July 2014

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.4809

zbMATH Keywords

completely integrable systemstoric degenerationpolygon triangulationGrassmannian space

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Lagrangian submanifolds; Maslov index (53D12) Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category (53D37)

Related Items (12)

Floer cohomology and flips ⋮ Convexity of Singular Affine Structures and Toric-Focus Integrable Hamiltonian Systems ⋮ Combinatorial mutations of Newton-Okounkov polytopes arising from plabic graphs ⋮ Exotic Lagrangian tori in Grassmannians ⋮ Immersed two-spheres and SYZ with application to Grassmannians ⋮ Disk potential functions for quadrics ⋮ Singular fibres of the Gelfand–Cetlin system on MANI( n )* ⋮ Open problems, questions and challenges in finite- dimensional integrable systems ⋮ On the Gromov width of polygon spaces ⋮ SYZ mirror symmetry for hypertoric varieties ⋮ Newton-Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians ⋮ Pseudotoric structures and special Lagrangian torus fibrations on certain flag varieties

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Potential functions via toric degenerations
• The symplectic geometry of polygons in Euclidean space
• Equivalence of mirror families constructed from toric degenerations of flag varieties
• Toric degenerations of Gelfand-Cetlin systems and potential functions
• Floer cohomology and disc instantons of Lagrangian torus fibers in Fano toric manifolds
• The Gelfand-Cetlin system and quantization of the complex flag manifolds
• Extended moduli spaces of flat connections on Riemann surfaces
• Polygon spaces and Grassmannians
• Tensor product multiplicities, canonical and totally positive varieties
• Geometry in Grassmannians and a generalization of the dilogarithm
• Symplectic toric space associated to triangle inequalities
• Lagrangian torus fibration of quintic Calabi-Yau hypersurfaces. II: Technical results on gradient flow construction
• Lagrangian Floer theory on compact toric manifolds. I.
• Gravitational Quantum Cohomology
• Lagrangian Floer theory and mirror symmetry on compact toric manifolds
• Special Lagrangian fibrations, wall-crossing, and mirror symmetry
• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• Moduli Spaces of Polygons and Punctured Riemann Spheres
• The Symplectic Geometry of Polygons in the 3-Sphere
• The tropical Grassmannian
• The Toric Geometry of Triangulated Polygons in Euclidean Space
• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Around polygons in \(\mathbb R^3\) and \(S^3\)

This page was built for publication: Toric degenerations of integrable systems on Grassmannians and polygon spaces