Gröbner geometry of Schubert polynomials
2005/05/01 by Allen Knutson, Ezra Miller · 35 citations
Mathematics · #Advanced Combinatorial Mathematics #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models
paper · pdf · doi:10.4007/annals.2005.161.1245
Abstract
Given a permutation w S n , we consider a determinantal ideal I w whose generators are certain minors in the generic n n matrix (filled with independent variables). Using 'multidegrees' as simple algebraic substitutes for torus-equivariant cohomology classes on vector spaces, our main theorems describe, for each ideal I w :
Cited by
- Gröbner geometry of Schubert polynomials through ice
- Celebrating Loday’s associahedron
- Back stable Schubert calculus
- Zero-one Schubert polynomials
- On some Grothendieck expansions
- Schubert Polynomials in Types A and C
- The Grothendieck Group of the Variety of Spanning Line Configurations
- Fine multidegrees, universal Grobner bases, and matrix Schubert varieties
- Finding all monomials in a polynomial ideal
- Plumbing bijections
- Heaps of rhombic dodecahedra, catalan congruences on alternating sign matrices, and bases of the Temperley-Lieb algebra
- Bumpless Pipe Dream Fragments -- Equivariant Geometry of Clans
- K-classes of Brill-Noether loci and a determinantal formula
- Algebraic geometry of Gaussian Bayesian networks
- The greedy flip tree of a subword complex
- Maximal 0-1 fillings of moon polyominoes with restricted chain-lengths\n and rc-graphs
- Torus Actions on Matrix Schubert and Kazhdan-Lusztig Varieties, and their Links to Statistical Models
- Complexity of the Zero Set of a Matrix Schubert Ideal
- Six-Vertex, Loop and Tiling models: Integrability and Combinatorics
- Combinatorial models for Schubert polynomials
- Hybrid pipe dreams for the lower-upper scheme
- Excited Young diagrams, equivariant K-theory, and Schubert varieties
- Regular cell complexes in total positivity
- Derivatives of padded Schubert polynomials through pipe dreams
- Schubert Classes in the Equivariant K-Theory and Equivariant Cohomology of the Grassmannian
- Kempf collapsing and quiver loci
- Proof of a conjectured Möbius inversion formula for Grothendieck polynomials
- When is a polynomial ideal binomial after an ambient automorphism?
- Positroid varieties I: juggling and geometry
- Chute Move Posets are Lattices
- A Proof of Rubey's Lattice Conjecture
- Schubert polynomials, the inhomogeneous TASEP, and evil-avoiding permutations
- Principal specializations of Schubert polynomials and pattern containment
- Syzygies of polymatroidal ideals
- Multiplicities of the Most Singular Point on Schubert varieties on Gl(n)/B for n=5,6
- Catalan numbers and Schubert polynomials for w=1(n+1)... 2
- Subword Complexes and Kalai's Conjecture on Reconstruction of Spheres. [europepmc]
Related