For a real-analytic generic submanifold M ⊂ [special characters omitted] of codimension k given by rjz,z&d1; =0,j=1,&ldots;,k Segre variety Q_w is defined as Q_w = {z : ρ_j( z, w¯) = 0, j = 1,…, k}. For a set A we define the polarization A* (with respect to M) as A* = {z : A⊂ Q_z}. The relation between A and A* is invariant under biholomorphic transformations of M and in most cases the analytic set A* is sparse since it is defined by an infinite system of equations. At the same time, the polarization could be rather large for some surfaces (for example, sphere in [special characters omitted]. In this thesis we study how large A* could get, relative to the size of analytic set A. In particular, we obtain the following result

Theorem. If a real-analytic generic submanifold M ⊂ [special characters omitted] of codimension k does not contain germs of analytic sets then locally the inequality dim A + dim A* ≤ n holds.

A large class of surfaces allowing the largest possible dual sets was found.

In the second part of the thesis we study in more detail real-analytic, finite type Levi-non-degenerate hypersurfaces in [special characters omitted] that allow large polarizations. In this setting we proved that existence of large enough family of 1-dimensional analytic sets with largest polarizations imposes geometric restrictions on the hypersurface.