Hamiltonian reductions as affine closures of cotangent bundles
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915757293568000 |
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| author | Fu, Baohua Liu, Jie |
| author_facet | Fu, Baohua Liu, Jie |
| contents | Let $Y$ be an irreducible non-singular affine $G$-variety with a $2$-large action. We show that the Hamiltonian reduction $T^*Y/\!\!/\!\!/G$ is a symplectic variety with terminal singularities, isomorphic to the affine closure of $T^*Z_{\text{reg}}$ where $Z:=Y/\!/G$. Furthermore, we provide sufficient conditions for the non-existence of a symplectic resolution for such varieties. These results yield three main applications: (i) providing a short proof of G. Schwarz's theorem on the graded surjectivity of the push-forward map $\mathcal{D}(Y)^G \to \mathcal{D}(Z)$; (ii) establishing the surjectivity of the symbol map on $Z$; and (iii) confirming the non-linear analog of a conjecture of Kaledin--Lehn--Sorger for $2$-large actions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03068 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hamiltonian reductions as affine closures of cotangent bundles Fu, Baohua Liu, Jie Algebraic Geometry Representation Theory 14B05, 53D20, 14L24, 14J42 Let $Y$ be an irreducible non-singular affine $G$-variety with a $2$-large action. We show that the Hamiltonian reduction $T^*Y/\!\!/\!\!/G$ is a symplectic variety with terminal singularities, isomorphic to the affine closure of $T^*Z_{\text{reg}}$ where $Z:=Y/\!/G$. Furthermore, we provide sufficient conditions for the non-existence of a symplectic resolution for such varieties. These results yield three main applications: (i) providing a short proof of G. Schwarz's theorem on the graded surjectivity of the push-forward map $\mathcal{D}(Y)^G \to \mathcal{D}(Z)$; (ii) establishing the surjectivity of the symbol map on $Z$; and (iii) confirming the non-linear analog of a conjecture of Kaledin--Lehn--Sorger for $2$-large actions. |
| title | Hamiltonian reductions as affine closures of cotangent bundles |
| topic | Algebraic Geometry Representation Theory 14B05, 53D20, 14L24, 14J42 |
| url | https://arxiv.org/abs/2601.03068 |