Resolution of symplectic cyclic orbifold singularities

TL;DR

This paper introduces a method for resolving symplectic orbifold singularities from Hamiltonian S^1-actions, demonstrating that all isolated cyclic singularities can be resolved and that pre-quantizations are fillable by smooth manifolds.

Contribution

It provides a systematic approach to resolve symplectic orbifold singularities and establishes fillability of pre-quantizations by smooth manifolds.

Findings

All isolated cyclic singularities admit resolutions.

Pre-quantizations of symplectic orbifolds are symplectically fillable.

Method applies to symplectic reduction at regular values.

Abstract

In this paper we present a method to obtain resolutions of symplectic orbifolds arising from symplectic reduction of a Hamiltonian S^1-manifold at a regular value. As an application, we show that all isolated cyclic singularities of a symplectic orbifold admit a resolution and that pre-quantisations of symplectic orbifolds are symplectically fillable by a smooth manifold.