Connected components of moduli spaces of irreducible holomorphic   symplectic manifolds of Kummer type
  Moduli spaces of polarised (with fixed polarisation type) irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on $K3$ surfaces are not connected in general and A. Apostolov counted the number of their components. We extend Apostolov's results to the case of manifolds deformation equivalent to generalised Kummer varieties. 
Claudio Onorati
math.AG