On the enumeration of complex plane curves with two singular points

Details On the enumeration of complex plane curves with two singular points On the enumeration of complex plane curves with two singular points

2007-08-09

arxiv.org/abs/0708.1229v5

International Mathematics Research Notices, 2010

Mathematics

Algebraic Geometry

24 pages, the Mathematica file with explicit calculations is attached. Some typos removed. To appear in the International Math

Scientific paper

10.1093/imrn/rnq057

We study equi-singular strata of plane curves with two singular points of prescribed types. The method of the previous work [Kerner06] 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.

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