Abstract
The group PGL(3) of linear transformations of the projective plane acts
naturally on the projective space parametrizing curves of a given
degree. In this note we begin the study of the orbits of smooth curves
under this action: we construct a resolution of the closure of the orbit
of a given curve, and we use it to compute its degree. This turns out to
depend only on the degree of the curve, the order of its automorphism
group, and on the number and type of its flexes. This paper will appear
on the Journal of Algebraic Geometry.
Original language | English |
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Journal | Journal of Algebraic Geometry |
Publication status | Published - 1 Jan 1993 |
Externally published | Yes |
Keywords
- Mathematics - Algebraic Geometry