A remark on isolated symplectic singularities with trivial local fundamental group

TL;DR

This paper presents a straightforward construction method for isolated symplectic singularities with trivial local fundamental groups across any dimension, expanding on recent examples and using toric hyperkähler techniques.

Contribution

It introduces a simple, general construction for isolated symplectic singularities with trivial local fundamental groups, applicable to any dimension, based on toric hyperkähler methods.

Findings

Constructed infinite series of symplectic singularities with trivial local fundamental group

Applicable to any dimension using toric hyperkähler construction

Simplifies previous complex constructions

Abstract

Recently, Bellamy et al. constructed an infinite series of 4-dimensional isolated symplectic sngularities with trivial local fundamental group, inspired by a question of Beauville. In this short note, we introduce an easy construction of isolated symplectic singularities (of any dimension) with trivial local fundamental group. We will use a toric hyperkaehler construction.