The differential equation satisfied by a plane curve of degree n
Combinatorics
2007-05-23 v1
Abstract
Eliminating the arbitrary coefficients in the equation of a generic plane curve of order by computing sufficiently many derivatives, one obtains a differential equation. This is a projective invariant. The first one, corresponding to conics, has been obtained by Monge. Sylvester, Halphen, Cartan used invariants of higher order. The expression of these invariants is rather complicated, but becomes much simpler when interpreted in terms of symmetric functions.
Keywords
Cite
@article{arxiv.math/0602380,
title = {The differential equation satisfied by a plane curve of degree n},
author = {Alain Lascoux},
journal= {arXiv preprint arXiv:math/0602380},
year = {2007}
}