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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.03012 |
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Table of Contents:
- Let $(X, ω)$ be a conical symplectic variety of dimension $2n$ 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. A typical example of $X$ is a toric hyperkahler variety $Y(A,0)$. In this article, we prove that this property characterizes $Y(A,0)$ with $A$ unimodular. More precisely, if $(X, ω)$ is such a conical symplectic variety, then there is a $T^n$-equivariant (complex analytic) isomorphism $φ: (X, ω) \to (Y(A,0), ω_{Y(A,0)})$ under which both moment maps are identified. Moreover $φ$ sends the center $0_X$ of $X$ to the center $0_{Y(A,0)}$ of $Y(A,0)$.