On rational cuspidal projective plane curves

In the open problem of classification of rational cuspidal plane curves it is essential to find good necessary conditions on the type of singularities of a curve C in order C to exit. Motivated by the study of the Seiberg-Witten invariant of normal surface singularities whose link is a rational homology sphere we have found good candidates for such necessary conditions. In this paper we study this compatibility conditions and proved them for all curves whose logarithmic Kodaira dimension is strictly less than 2.