Based on a joint work with Y.Namikawa sensei cf., https://arxiv.org/pdf/2503.15791.

Symplectic singularities arise from e.g., nilpotent orbit closure, compact hyperKahler varieties, quiver varieties, and so on. D.Kaledin conjectured symplectic singularities are all "conical" shapes in the sense that they admit torus action with positive weights, around 2 decades ago. Our paper provides a new approach (resp., affirmative solution) to this problem (in many cases) via complex differential geometry and related K-stability theory in algebraic geometry, combined with Poisson deformation theory. This approach/resolution has a benefit to substantially strengthen the statements - to take the torus action as canonical action, compatible with hyperKahler metric rescaling structure.