The differential equation satisfied by a plane curve of degree n

Details The differential equation satisfied by a plane curve of degree n The differential equation satisfied by a plane curve of degree n

2006-02-17

arxiv.org/abs/math/0602380v1

Mathematics

Combinatorics

Scientific paper

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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