English

Commuting Schemes of Upper Triangular Matrices and Representation Homology

Algebraic Geometry 2025-10-23 v3 Commutative Algebra Algebraic Topology

Abstract

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

Keywords

Cite

@article{arxiv.2403.13953,
  title  = {Commuting Schemes of Upper Triangular Matrices and Representation Homology},
  author = {Guanyu Li},
  journal= {arXiv preprint arXiv:2403.13953},
  year   = {2025}
}

Comments

Final version, 15 pages

R2 v1 2026-06-28T15:27:57.289Z