PLANE CURVES WITH SMALL LINEAR ORBITS II-Reference-Cited by-同舟云学术

PLANE CURVES WITH SMALL LINEAR ORBITS II

Published:2000-07 Issue:05 Volume:11 Page:591-608
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

ALUFFI PAOLO¹,FABER CAREL²³

Affiliation:

1. Mathematics Department, Florida State University, Tallahassee FL 32306, USA

2. Department of Mathematics, Oklahoma State University, Stillwater OK 74078, USA

3. Department of Mathematics, KTH, 100 44 Stockholm, Sweden

Abstract

The "linear orbit" of a plane curve of degree d is its orbit in ℙd(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 [3], 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X00000301

Reference5 articles.

1. The Enumerative Geometry of Plane Cubics. I: Smooth Cubics

2. Varieties of strange plane curves

3. Ueber diejenigen ebenen Curven, welche durch ein geschlossenes System von einfach unendlich vielen vertauschbaren linearen Transformationen in sich �bergehen

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