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Plane curves with small linear orbits, I

Paoli Aluffi; Carel Faber — 2000

Annales de l'institut Fourier

The “linear orbit” of a plane curve of degree $d$ is its orbit in $ℙ^{d (d + 3) / 2}$ 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...

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