The XVI-th Hilbert problem about limit cycles
1. Introduction. The XVI-th Hilbert problem consists of two parts. The first part concerns the real algebraic geometry and asks about the topological properties of real algebraic curves and surfaces. The second part deals with polynomial planar vector fields and asks for the number and position of limit cycles. The progress in the solution of the first part of the problem is significant. The classification of algebraic curves in the projective plane was solved for degrees less than 8. Among general...