A recursive formula for osculating curves (Q2032829)

Gromov-Witten theory is used to prove an interesting result in enumerative geometry that generalizes old theorems of \textit{G. Salmon} [A treatise on the analytic geometry of three dimensions. Hodges, Smith, and Company (1865); see revised by R. A. P. \textit{Rogers}. Fifth edition, in 2 vols. Vol. I. London: Longmans, Green \& Co (1911; JFM 42.0587.01)] and \textit{G. Darboux} [Darboux Bull. (2) 4, 348--384 (1880; JFM 12.0590.01)].