Plane curves with small linear orbits II

Details Plane curves with small linear orbits II Plane curves with small linear orbits II

1999-06-19

arxiv.org/abs/math/9906131v2

Internat. J. Math. 11 (2000), no. 5, 591-608

Mathematics

Algebraic Geometry

16 pages, one figure. Proof of main result expanded, references added

Scientific paper

10.1142/S0129167X00000301

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). We classify curves with positive dimensional stabilizer, and we compute the degree of the closure of the linear orbits of curves supported on unions of lines. Together with the results of math.AG/9805020, this encompasses the enumerative geometry of all plane curves with small linear orbit. This information will serve elsewhere as an ingredient in the computation of the degree of the orbit closure of an arbitrary plane curve.

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