Nicholas J. Willis, David A. Weinberg
Published 2019-06-26Version 1
For real irreducible algebraic curves of the seventh degree, there are 22 types of singular points of multiplicity six, 174 types of singular points of multiplicity five, and at least 182 types of singular points of multiplicity four. For complex irreducible algebraic curves of the seventh degree, there are 12 types of singular points of multiplicity six, 92 types of singular points of multiplicity five, and at least 92 types of singular points of multiplicity four. In the final section of the paper, a wide variety of open problems on the classification of singular points of plane algebraic cuves is explicitly described.
Number of singular points of a genus $g$ curve with one point at infinity
Number of singular points of an annulus in $\mathbb{C}^2$
Singular points of real quartic curves via computer algebra
![QR code for arXiv:1906.11214 [math.AG]](http://oss.arxitics.com/images/favicon.svg)