Equivariant cohomology of Grassmannian spanning lines

2024/10/02 by Chou, Raymond, Matsumura, Tomoo, Rhoades, Brendon · 2 citations
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.02105

Abstract

Given integers n ≥ k ≥ d, let X_n,k,d be the moduli space of n-tuples of lines (ℓ₁, …, ℓ_n) in ℂ^k such that ℓ₁ + ⋯ + ℓ_n has dimension d. We give a quotient presentation of the torus-equivariant cohomology of X_n,k,d. The form of this presentation, and in particular the torus parameters appearing therein, will arise from the orbit harmonics method of combinatorial deformation theory.

Cited by

• The Grothendieck Group of the Variety of Spanning Line Configurations
• Big Varchenko-Gelfand rings and orbit harmonics

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