Plane curves with small linear orbits, I

Aluffi, Paoli, and Faber, Carel. "Plane curves with small linear orbits, I." Annales de l'institut Fourier 50.1 (2000): 151-196. <http://eudml.org/doc/75411>.

@article{Aluffi2000,
abstract = {The “linear orbit” of a plane curve of degree $d$ is its orbit in $\{\Bbb P\}^\{d(d+3)/2\}$ under the natural action of $\{\rm PGL\}(3)$. 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.},
author = {Aluffi, Paoli, Faber, Carel},
journal = {Annales de l'institut Fourier},
keywords = {projective linear group; degree; stabilizer; blow-up; orbit closure; PGL(3)-orbit; enumerative geometry of plane curves},
language = {eng},
number = {1},
pages = {151-196},
publisher = {Association des Annales de l'Institut Fourier},
title = {Plane curves with small linear orbits, I},
url = {http://eudml.org/doc/75411},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Aluffi, Paoli
AU - Faber, Carel
TI - Plane curves with small linear orbits, I
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 1
SP - 151
EP - 196
AB - The “linear orbit” of a plane curve of degree $d$ is its orbit in ${\Bbb P}^{d(d+3)/2}$ under the natural action of ${\rm PGL}(3)$. 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.
LA - eng
KW - projective linear group; degree; stabilizer; blow-up; orbit closure; PGL(3)-orbit; enumerative geometry of plane curves
UR - http://eudml.org/doc/75411
ER -