On the enumeration of complex plane curves with two singular points
Algebraic Geometry
2010-06-02 v5
Abstract
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.
Cite
@article{arxiv.0708.1229,
title = {On the enumeration of complex plane curves with two singular points},
author = {Dmitry Kerner},
journal= {arXiv preprint arXiv:0708.1229},
year = {2010}
}
Comments
24 pages, the Mathematica file with explicit calculations is attached. Some typos removed. To appear in the International Mathematics Research Notices