The differential equation satisfied by a plane curve of degree n

2006/02/17 by Alain Lascoux, Lascoux, Alain
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Combinatorics #Combinatorics (math.CO) #Differential Equations #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.math/0602380

arxiv created 2006/02/17 · openalex publication_date 2006/02/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Eliminating the arbitrary coefficients in the equation of a generic plane curve of order n 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.

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