MathDBHyperkähler cone conjecture for conical symplectic singularities
Hyperkähler cone conjecture for conical symplectic singularities
A conical symplectic singularity is a symplectic singularity equipped with a conical structure. A hyperkähler cone is a cone carrying a hyperkähler structure compatible with its dilation action.
Hyperkähler cone conjecture. Any conical symplectic singularity is a hyperkähler cone.
This is presented as a conjecture suggested by the Yau–Tian–Donaldson correspondence for K-polystable Fano cones and Ricci-flat Kähler cones. Its status is not resolved in the supplied text.
Sources & referencesView supporting material
Primary source
Chenyang Xu, Ziquan Zhuang and Henri Guenancia, “Stable Degeneration, Non-degenerate Forms, and Kaledin's Conjecture”, arXiv:2606.02401 (2026).
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