Newton-Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians
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Publication:2302614
DOI10.1215/00127094-2019-0028zbMath1439.14142arXiv1712.00447OpenAlexW2771406229MaRDI QIDQ2302614
Konstanze Rietsch, Lauren K. Williams
Publication date: 26 February 2020
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1712.00447
Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Grassmannians, Schubert varieties, flag manifolds (14M15) Cluster algebras (13F60) Mirror symmetry (algebro-geometric aspects) (14J33)
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Cites Work
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- Minkowski polynomials and mutations
- Convex bodies appearing as Okounkov bodies of divisors
- Poisson structures compatible with the cluster algebra structure in Grassmannians
- Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory
- Integer decomposition property of dilated polytopes
- KP solitons and total positivity for the Grassmannian
- SAGBI bases and degeneration of spherical varieties to toric varieties
- Cyclic sieving and cluster duality of Grassmannian
- Matching polytopes, toric geometry, and the totally non-negative Grassmannian.
- Geometry of canonical bases and mirror symmetry
- Integrable systems, toric degenerations and Okounkov bodies
- Crystal bases and Newton-Okounkov bodies
- Total positivity in Schubert varieties
- Mirror symmetry and toric degenerations of partial flag manifolds
- Tropical critical points of the superpotential of a flag variety
- Donaldson-Thomas transformations of moduli spaces of G-local systems
- Cluster algebras. III: Upper bounds and double Bruhat cells.
- Toric degenerations of spherical varieties
- Toric degenerations of \(\mathrm{Gr}(2, n)\) and \(\mathrm{Gr}(3, 6)\) via plabic graphs
- Brunn-Minkowski inequality for multiplicities
- Parametrizations of canonical bases and totally positive matrices
- The \(B\)-model connection and mirror symmetry for Grassmannians
- Positivity for cluster algebras
- Okounkov bodies and toric degenerations
- Affine approach to quantum Schubert calculus
- The tropical totally positive Grassmannians
- Network parametrizations for the Grassmannian
- Cluster ensembles and Kac-Moody groups
- A mirror symmetric construction of \(qH_T^*(G/P)_{(q)}\)
- Moduli spaces of local systems and higher Teichmüller theory
- Twists of Plücker coordinates as dimer partition functions
- Gravitational Quantum Cohomology
- Cluster algebras I: Foundations
- Positroid varieties: juggling and geometry
- Algebraic Equations and Convex Bodies
- A Field of Generalised Puiseux Series for Tropical Geometry
- Canonical bases for cluster algebras
- Introduction to Toric Varieties. (AM-131)
- Birational geometry of cluster algebras
- GRASSMANNIANS AND CLUSTER ALGEBRAS
- A Mirror Construction for the Totally Nonnegative Part of the Peterson Variety
- Cluster algebras IV: Coefficients
- Canonical Bases Arising from Quantized Enveloping Algebras
- A Formula for Plucker Coordinates Associated with a Planar Network
- Convex bodies associated to linear series
- Cluster ensembles, quantization and the dilogarithm
- Stationary Phase Integrals, Quantum Toda Lattices, Flag Manifolds and the Mirror Conjecture
- The twist for positroid varieties
- On the quantum product of Schubert classes
- Degree bounds in quantum Schubert calculus
- Convex bodies associated to actions of reductive groups
- Toric degenerations of cluster varieties and cluster duality
- Toric degenerations of integrable systems on Grassmannians and polygon spaces
- Khovanskii Bases, Higher Rank Valuations, and Tropical Geometry
- Introduction to quantum groups