Symplectic singularity as hyperKähler cone

We prove that any symplectic singularity has a structure of hyperKähler cone. In particular, it is equivalent to the vertex of a conical symplectic variety, and it is automatically K-polystable.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-26
DOI
https://doi.org/10.48550/arxiv.2610.35510
Primary Topic
Geometry and complex manifolds
Type
preprint
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preprint

Symplectic singularity as hyperKähler cone

Yuji Odaka
arXiv (Cornell University)
Geometry and complex manifolds
preprint

Symplectic singularity as hyperKähler cone

Yuji Odaka
preprint en

Abstract

We prove that any symplectic singularity has a structure of hyperKähler cone. In particular, it is equivalent to the vertex of a conical symplectic variety, and it is automatically K-polystable.

arXiv (Cornell University)
Geometry and complex manifolds
DOIOpen Access PDFOpenAlex
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Symplectic singularity as hyperKähler cone — Yuji Odaka · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS