Plane curves with small linear orbits, I
Annales de l'Institut Fourier, Volume 50 (2000) no. 1, pp. 151-196.

The “linear orbit” of a plane curve of degree d is its orbit in d(d+3)/2 under the natural action of PGL (3). In this paper we compute the degree of the closure of the linear orbits of most curves with positive dimensional stabilizers. Our tool is a nonsingular variety dominating the orbit closure, which we construct by a blow-up sequence mirroring the sequence yielding an embedded resolution of the curve. The results given here will serve as an ingredient in the computation of the analogous information for arbitrary plane curves. Linear orbits of smooth plane curves were studied by the authors in J. of Alg. Geom., 2 (1993), 155-184.

L’“orbite linéaire” d’une courbe plane de degré d est son orbite dans d(d+3)/2 pour l’action naturelle de PGL (3). Dans cet article nous calculons le degré de l’adhérence de l’orbite linéaire pour la plupart des courbes dont le stabilisateur est de dimension positive. Nous utilisons une variété non singulière dominant l’adhérence de l’orbite, que nous construisons par une suite d’éclatements qui reflète la suite produisant une résolution plongée de la courbe. Les résultats obtenus ainsi seront utiles à la détermination de l’information analogue pour les courbes planes quelconques. Les orbites linéaires des courbes planes lisses ont été étudiées par les auteurs dans J. of Alg. Geom., 2 (1993), 155-184.

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Aluffi, Paoli; Faber, Carel. Plane curves with small linear orbits, I. Annales de l'Institut Fourier, Volume 50 (2000) no. 1, pp. 151-196. doi : 10.5802/aif.1750. http://www.numdam.org/articles/10.5802/aif.1750/

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