Towards a characterization of toric hyperkähler varieties among symplectic singularities II
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913006644887552 |
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| author | Namikawa, Yoshinori |
| author_facet | Namikawa, Yoshinori |
| contents | This is a continuation of arXiv: 2408.03012. We answer affirmatively Question 5.10 posed in the previous article. More precisely, let $(X, ω)$ be a conical symplectic variety of dimension $2n$ with $wt(ω) = 2$, which has a projective symplectic resolution. Assume that $X$ admits an effective Hamiltonian action of an $n$-dimensional algebraic torus $T^n$, compatible with the conical $\mathbf{C}^*$-action. Then we prove that there is a $T^n$-equivariant algebraic isomorphism $(X, ω) \cong (Y(A,0), ω_{Y(A,0)})$ for a toric hyperkahler variety $Y(A, 0)$ with $A$ unimodular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27454 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Towards a characterization of toric hyperkähler varieties among symplectic singularities II Namikawa, Yoshinori Algebraic Geometry 14, 32 This is a continuation of arXiv: 2408.03012. We answer affirmatively Question 5.10 posed in the previous article. More precisely, let $(X, ω)$ be a conical symplectic variety of dimension $2n$ with $wt(ω) = 2$, which has a projective symplectic resolution. Assume that $X$ admits an effective Hamiltonian action of an $n$-dimensional algebraic torus $T^n$, compatible with the conical $\mathbf{C}^*$-action. Then we prove that there is a $T^n$-equivariant algebraic isomorphism $(X, ω) \cong (Y(A,0), ω_{Y(A,0)})$ for a toric hyperkahler variety $Y(A, 0)$ with $A$ unimodular. |
| title | Towards a characterization of toric hyperkähler varieties among symplectic singularities II |
| topic | Algebraic Geometry 14, 32 |
| url | https://arxiv.org/abs/2603.27454 |