Resolution of symplectic cyclic orbifold singularities

Abstract

In this paper we present a method to obtain resolutions of symplectic orbifolds arising from symplectic reduction of a Hamiltonian $S1$-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-quantizations of symplectic orbifolds are symplectically fillable by a smooth manifold.