Extension of 2-forms and symplectic varieties
  This paper deals with symplectic varieties which do not have symplectic resolutions. Some moduli spaces of semi-stable torsion-free sheaves on a K3 surface, and symplectic V-manifolds are such varieties.   We shall prove local Torelli theorem for symplectic varieties. Some results on symplectic singularities are also included. 
Yoshinori Namikawa