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We show how to construct a resolution of symplectic orbifolds obtained asquotients of presymplectic manifolds with a torus action. As a corollary, thisallows us to desingularise generic symplectic quotients. Given a manifold witha Hamiltonian action of a compact Lie group, symplectic reduction at acoadjoint orbit which is transverse to the moment map produces a symplecticorbifold. If moreover the points of this coadjoint orbit are regular elementsof the Lie coalgebra, that is, their stabiliser is a maximal torus, the resultfor torus quotients may be applied to obtain a desingularisation of thesesymplectic orbifolds. Regular elements of the Lie coalgebra are generic in thesense that the singular strata have codimension at least three.  Additionally, we show that even though the result of a symplectic cut is anorbifold, it can be modified in an arbitrarily small neighbourhood of the cuthypersurface to obtain a smooth symplectic manifold.

Desingularisation of orbifolds obtained from symplectic reduction at generic coadjoint orbits