cyclic_orbifold Resolution of symplectic cyclic orbifold singularities Klaus Niederkrüger Federica Pasquotto http://dx.doi.org/10.4310/JSG.2009.v7.n3.a4 J. of Symplectic Geom. 7 (2009), no. 3, 337-355. 2009 JSG.jpg
In this paper we present a method to obtain resolutions of symplectic orbifolds arising as quotients of pre-symplectic semi-free S1-actions. This includes, in particular, all orbifolds arising from symplectic reduction of Hamiltonian S1-manifolds at regular values, as well as all isolated cyclic orbifold singularities.
As an application, we show that pre-quantisations of symplectic orbifolds are symplectically fillable by a smooth manifold.
DISCLAIMER: Contrary to what is claimed in "Symplectic resolutions, Lefschetz property and formality" by G. Cavalcanti, M. Fernández, and V. Muñoz, their result does not render our construction useless. The main innovation in their resolution method consists in only studying orbifolds with isolated singularities and ignoring more difficult singularities.