Combinatorial Models for the Variety of Complete Quadrics

2016/10/09 by Soumya Banerjee, Banerjee, Soumya, Mahir Bilen Can +3
Engineering · Mathematics · #05A05 #14M27 #19E08 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1610.02698

openalex publication_date 2016/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop several combinatorial models that are useful in the study of the SL_n-variety X of complete quadrics. Barred permutations parameterize the fixed points of the action of a maximal torus T of SL_n, while μ-involutions parameterize the orbits of a Borel subgroup of SL_n. Using these combinatorial objects, we characterize the T-stable curves and surfaces on X, compute the T-equivariant K-theory of X, and describe a Białynicki-Birula cell decomposition for X. Furthermore, we give a computational characterization of the Bruhat order on Borel orbits in X.

Related

• Ordered Bell numbers, Hermite polynomials, Skew Young Tableaux, and Borel orbits
• SL(2)-regular Subvarieties of Complete Quadrics
• Combinatorics and Quotients of Toric Varieties
• Selected topics on Toric Varieties
• Weak Order on Complete Quadrics