Equivariant Maximal Cohen-Macaulay sheaves on the minimal orbit closures
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866916047025602560 |
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| author | Xu, Shang |
| author_facet | Xu, Shang |
| contents | In this paper, we study maximal Cohen-Macaulay sheaves on closures of minimal nilpotent orbits in simple Lie algebras. For singularities of type $A_n$, we first classify vector bundles on their symplectic resolutions whose pushforwards are maximal Cohen-Macaulay. We then construct equivariant maximal Cohen-Macaulay sheaves via irreducible representations of the stabilizer group. We compare these two approaches in the case of maximal Cohen-Macaulay Weil divisors, and extend the equivariant construction to the classical types $B_n$, $C_n$, and $D_n$. Finally, we formulate the construction for an arbitrary simple Lie algebra and carry it out explicitly in the exceptional cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26565 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equivariant Maximal Cohen-Macaulay sheaves on the minimal orbit closures Xu, Shang Algebraic Geometry Commutative Algebra Representation Theory 14B05, 14M17, 14F06, 17B08, 20G05 In this paper, we study maximal Cohen-Macaulay sheaves on closures of minimal nilpotent orbits in simple Lie algebras. For singularities of type $A_n$, we first classify vector bundles on their symplectic resolutions whose pushforwards are maximal Cohen-Macaulay. We then construct equivariant maximal Cohen-Macaulay sheaves via irreducible representations of the stabilizer group. We compare these two approaches in the case of maximal Cohen-Macaulay Weil divisors, and extend the equivariant construction to the classical types $B_n$, $C_n$, and $D_n$. Finally, we formulate the construction for an arbitrary simple Lie algebra and carry it out explicitly in the exceptional cases. |
| title | Equivariant Maximal Cohen-Macaulay sheaves on the minimal orbit closures |
| topic | Algebraic Geometry Commutative Algebra Representation Theory 14B05, 14M17, 14F06, 17B08, 20G05 |
| url | https://arxiv.org/abs/2605.26565 |