Commuting Schemes of Upper Triangular Matrices and Representation Homology
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911226800373760 |
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| author | Li, Guanyu |
| author_facet | Li, Guanyu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13953 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Commuting Schemes of Upper Triangular Matrices and Representation Homology Li, Guanyu Algebraic Geometry Commutative Algebra Algebraic Topology 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. |
| title | Commuting Schemes of Upper Triangular Matrices and Representation Homology |
| topic | Algebraic Geometry Commutative Algebra Algebraic Topology |
| url | https://arxiv.org/abs/2403.13953 |