On the enumeration of complex plane curves with two singular points
نویسنده
چکیده
We study equi-singular strata of curves with two singular points of prescribed types. The method of our previous work [Kerner04] is generalized to this case. This allows to solve the enumerative problem for plane curves with two singular points of linear singularity types. In the general case this reduces the enumerative questions to the problem of collision of the two singular points. The method is applied to several cases, e.g. enumeration of curves with two ordinary multiple points, with a point of a linear singularity type and a node etc. Explicit numerical results are given. A trivial consequence of the method is the determination of Thom polynomials for curves with one singular point (for some series of singularity types). Some examples are given. MSC: primary -14N10, 14N35 secondary -14H10, 14H50
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