Arnold's seminar, Moscow University, April 19, 2005 Leonid Stunzhas {aspirant 1 goda kaf. Dynamical systems) Singularities of center symmetry set Center symmetry set of a smooth hypersurface in an affine space is the envelope of lines joining pairs of the hypersurface points with parallel tangent hyperplanes. A projetive generalization of this object for curves, its generic singularities will be discussed. Some computer calculation of dimensions of relevant varieties will be presented. --- http://www.pdmi.ras.ru/~arnsem