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Plane curves with small linear orbits. I. (English) Zbl 0953.14030

Let \(C \subset \mathbb{P}^2\) be a reduced plane curve. Here the authors classify all such \(C\) which are not union of lines and such that their orbit for the natural action of PGL(3) has dimension \(\leq 7\). This work is significant for the enumerative geometry of plane curves and in particular for the computation of the degree of the orbit closure of an arbitrary plane curve. Fur further works by the authors, see P. Aluffi and C. Faber, “Plane curves with small linear orbits. II”, e-prints math.AG/9906131 and “Linear orbits of arbitrary plane plane curves”, math.AG/9912092.
Reviewer: E.Ballico (Povo)

MSC:

14N10 Enumerative problems (combinatorial problems) in algebraic geometry
14H50 Plane and space curves
14L30 Group actions on varieties or schemes (quotients)
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References:

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