Commuting Schemes of Upper Triangular Matrices and Representation Homology

2024/03/20 by Li, Guanyu
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.13953

Abstract

We establish a connection between generalised commuting schemes C_g(U_n) of higher genus g, which are associated with a group scheme U_n consisting of upper triangular unipotent matrices, and the representation homology HR_*(Σ_g,U_n) of a Riemann surface Σ_g with coefficients in the group U_n. As an outcome, we provide a numerical criterion for determining whether commuting schemes C(U_n) form a complete intersection.

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