  Local symplectic contractions are resolutions of singularities which admit
symplectic forms. Four dimensional symplectic contractions are (relative) Mori
Dream Spaces. In particular, any two such resolutions of a given singularity
are connected by a sequence of Mukai flops. We discuss the cone of movable
divisors on such a resolution; its faces are determined by curves whose loci
are divisors, we call them essential curves. The movable cone is divided into
nef chambers which are related to different resolutions; this subdivision is
determined by classes of 1-cycles. We also study schemes parametrizing minimal
essential curves and show that they are resolutions, possibly non-minimal, of
surface Du Val singularities. Some examples, with an exhaustive description,
are provided.
