On the Enumeration of Complex Plane Curves with Two Singular Points

We study equisingular strata of plane curves with two singular points of prescribed types. The method of the previous work [25] is generalized to this case. In particular, we consider the enumerative problem for plane curves with two singular points of linear singularity types. First, the problem for two ordinary multiple points of fixed multiplicities is solved. Then the enumeration for arbitrary linear types is reduced to the case of ordinary multiple points and to the understanding of "merging" of singular points. Many examples and numerical answers are given.