Towards a characterization of toric hyperkähler varieties among symplectic singularities

• Yoshinori Namikawa ^[1]
  1. [1] Research Institute for Mathematical Sciences, Kyoto University, Oiwake-cho, Kyoto, Japan
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 32, Nº. 1, 2026
• Idioma: inglés
• DOI: 10.1007/s00029-025-01118-6
• Enlaces
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• Resumen

  • 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 C∗-action. A typical example of X is a toric hyperkähler 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) → (Y (A, 0), ωY (A,0)) under which both moment maps are identified. Moreover, ϕ sends the center 0X of X to the center 0Y (A,0) of Y (A, 0).

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