Asymptotic growth of the number of classes of real plane algebraic   curves when the degree increases
  The nonsingular real plane algebraic curves of given degree $d$ are considered either up to isotopy or up to deformation. The asymptotic behavior of the number $I_d$ of isotopy classes and the number $D_d$ of deformation classes are studied. It is shown, in particular, that $log I_d\asypt d^2$. Other related problems and their higher dimensional generalisations are discussed. 
S.Yu.Orevkov, V.M.Kharlamov