Viatcheslav Kharlamov, Université de Strasbourg
In ongoing work with Rares Rasdeaconu we explore the maximality of the Hilbert square of maximal real varieties. We found that starting from dimension 2 many of deformation classes of algebraic varieties do not contain any real variety whose Hilbert square is maximal. For example, the K3-surfaces have never a maximal Hilbert square. In this talk I intend to outline the current state of our knowledge on this subject.