A note on symplectic singularities

TL;DR

This paper proves that the singular locus of a symplectic singularity cannot have codimension 3, and characterizes when such singularities are terminal based on the codimension of their singular locus.

Contribution

It establishes a new geometric property of symplectic singularities, specifically regarding the codimension of their singular loci and conditions for terminality.

Findings

Singular locus of a symplectic singularity has no codimension 3 components.

A symplectic singularity is terminal iff its singular locus has codimension at least 4.

Provides insight into the structure and properties of symplectic singularities.

Abstract

In this paper we shall prove that the singular locus of a symplectic singularity has no codimension 3 irreducible components. As a corollary, a symplectic singularity is terminal if and only if its singular locus has codimension $\geq 4$. It is hoped that a symplectic singularity has much stronger properties.