Plane curves with small linear orbits I

Details Plane curves with small linear orbits I Plane curves with small linear orbits I

1998-05-05

arxiv.org/abs/math/9805020v2

Ann. Inst. Fourier (Grenoble) 50 (2000), no. 1, 151-196

Mathematics

Algebraic Geometry

34 pages, 4 figures, AmS-TeX 2.1, requires xy-pic and epsf

Scientific paper

The `linear orbit' of a plane curve of degree d is its orbit in the projective space of dimension d(d+3)/2 parametrizing such curves 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 are studied in [A-F1].

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