Séminaire Lotharingien de Combinatoire, 93B.43 (2025), 12 pp.
Raymond Chou, Tomoo Matsumura and Brendon Rhoades
Equivariant Cohomology of Grassmannian Spanning Lines
Abstract.
For positive integers d ≤ k ≤ n, let Xn,k,d be the moduli space of n-tuples (ℓ1, ..., ℓn) of lines in Ck such that ℓ1 + ... + ℓn has vector space dimension d. The space Xn,k,d carries an action of the rank k torus
T = (C*)k, and we present the T-equivariant cohomology of Xn,k,d. This solves a problem of Pawlowski and Rhoades. Our methods feature the orbit harmonics technique of combinatorial deformation theory and suggest a relationship between orbit harmonics and equivariant cohomology.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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