Khovanskii Bases, Higher Rank Valuations, and Tropical Geometry
From MaRDI portal
Publication:5234528
DOI10.1137/17M1160148zbMath1423.13145arXiv1610.00298MaRDI QIDQ5234528
Christopher Manon, Kiumars Kaveh
Publication date: 27 September 2019
Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1610.00298
Gröbner basisSAGBI basisvaluationtropical geometryNewton-Okounkov bodytoric degenerationKhovanskii basissubduction algorithm
Lua error in Module:PublicationMSCList at line 37: attempt to index local 'msc_result' (a nil value).
Related Items (47)
Certification for polynomial systems via square subsystems ⋮ Standard monomial theory and toric degenerations of Richardson varieties in the Grassmannian ⋮ Combinatorial mutations and block diagonal polytopes ⋮ A new class of finitely generated polynomial subalgebras without finite SAGBI bases ⋮ Towards cluster duality for Lagrangian and orthogonal Grassmannians ⋮ KP solitons from tropical limits ⋮ Gelfand-Tsetlin degenerations of representations and flag varieties ⋮ Toric degenerations of Grassmannians and Schubert varieties from matching field tableaux ⋮ Numerical homotopies from Khovanskii bases ⋮ Toric degenerations of partial flag varieties and combinatorial mutations of matching field polytopes ⋮ Toric degenerations of low-degree hypersurfaces ⋮ Reflexivity of Newton–Okounkov bodies of partial flag varieties ⋮ Seshadri stratifications and standard monomial theory ⋮ Combinatorial mutations of Newton-Okounkov polytopes arising from plabic graphs ⋮ Combinatorial mutations of Gelfand-Tsetlin polytopes, Feigin-Fourier-Littelmann-Vinberg polytopes, and block diagonal matching field polytopes ⋮ Khovanskii-finite valuations, rational curves, and torus actions ⋮ Newton-Okounkov bodies of chemical reaction systems ⋮ Cox rings of projectivized toric vector bundles and toric flag bundles ⋮ Cluster duality for Lagrangian and orthgonal Grassmannians ⋮ Towards Landau-Ginzburg models for cominuscule spaces via the exceptional cominuscule family ⋮ Toric geometry. Abstracts from the workshop held March 27 -- April 2, 2022 ⋮ A Fano compactification of the \(\mathrm{SL}_2(\mathbb{C})\) free group character variety ⋮ Adjacency for scattering amplitudes from the Gröbner fan ⋮ Invariants for level-1 phylogenetic networks under the Cavendar-Farris-Neyman model ⋮ Khovanskii-finite rational curves of arithmetic genus 2 ⋮ Khovanskii bases for semimixed systems of polynomial equations -- approximating stationary nonlinear Newtonian dynamics ⋮ Stability of equivariant vector bundles over toric varieties ⋮ Tannakian classification of equivariant principal bundles on toric varieties ⋮ Standard monomial theory and toric degenerations of Schubert varieties from matching field tableaux ⋮ Quadratic Gröbner bases of block diagonal matching field ideals and toric degenerations of Grassmannians ⋮ Gröbner fans of Hibi ideals, generalized Hibi ideals and flag varieties ⋮ Families of Gröbner degenerations, Grassmannians and universal cluster algebras ⋮ Toric degenerations of flag varieties from matching field tableaux ⋮ Toric co-Higgs sheaves ⋮ Toric degenerations of Grassmannians from matching fields ⋮ Generic tropical initial ideals of Cohen-Macaulay algebras ⋮ Birational sequences and the tropical Grassmannian ⋮ Towards classifying toric degenerations of cubic surfaces ⋮ Gröbner theory and tropical geometry on spherical varieties ⋮ Cones from quantum groups to tropical flag varieties ⋮ Newton-Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians ⋮ Wonderful compactification of character varieties ⋮ The geometry of gaussoids ⋮ Well-poised hypersurfaces ⋮ The Dubrovin threefold of an algebraic curve ⋮ Seshadri stratification for Schubert varieties and standard monomial theory ⋮ Tropical geometry and Newton–Okounkov cones for Grassmannian of planes from compactifications
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Skeletons and tropicalizations
- Okounkov bodies for ample line bundles with applications to multiplicities for group representations
- Semigroups of \(sl_3(\mathbb C)\) tensor product invariants
- Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory
- SAGBI bases and degeneration of spherical varieties to toric varieties
- Hahn analytification and connectivity of higher rank tropical varieties
- Analytification is the limit of all tropicalizations
- Crystal bases and Newton-Okounkov bodies
- Elimination theory for tropical varieties
- Sagbi bases of Cox-Nagata rings
- Numerical Schubert calculus
- Toric degenerations of Schubert varieties
- Toric degenerations of spherical varieties
- Toric degenerations of \(\mathrm{Gr}(2, n)\) and \(\mathrm{Gr}(3, 6)\) via plabic graphs
- Computing bases for rings of permutation-invariant polynomials
- Khovanskii-finite valuations, rational curves, and torus actions
- Newton-Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians
- The total coordinate ring of a wonderful variety
- Okounkov bodies and toric degenerations
- Favourable modules: filtrations, polytopes, Newton-Okounkov bodies and flat degenerations
- Resolution of singularities of an algebraic variety over a field of characteristic zero. I
- Gelfand-Tsetlin degenerations of representations and flag varieties
- Newton-Okounkov polyhedra for character varieties and configuration spaces
- Algebraic Equations and Convex Bodies
- Okounkov Bodies of Finitely Generated Divisors
- On the structure of non-archimedean analytic curves
- CONTRACTION OF THE ACTIONS OF REDUCTIVE ALGEBRAIC GROUPS
- Canonical bases for cluster algebras
- ORDERED ABELIAN GROUPS
- Lectures on Resolution of Singularities (AM-166)
- Compactification of the moduli space of hyperplane arrangements
- Canonical Bases Arising from Quantized Enveloping Algebras
- Polytopes, Rings, and K-Theory
- Convex bodies associated to linear series
- The tropical Grassmannian
- Mixed volume and an extension of intersection theory of divisors
- Ideals, Varieties, and Algorithms
- Toric Geometry ofSL2(ℂ) Free Group Character Varieties from Outer Space
- Compactifications of subvarieties of tori
- Newton–Okounkov Bodies over Discrete Valuation Rings and Linear Systems on Graphs
- On Degenerations of Projective Varieties to Complexity-One T-Varieties
This page was built for publication: Khovanskii Bases, Higher Rank Valuations, and Tropical Geometry