Limits of PGL(3)-translates of plane curves, II

Details Limits of PGL(3)-translates of plane curves, II Limits of PGL(3)-translates of plane curves, II

2007-06-09

arxiv.org/abs/0706.1304v4

J. Pure Appl. Algebra 214 (2010), no. 5, 548-564

Mathematics

Algebraic Geometry

22 pages. Minor revision. Final version

Scientific paper

10.1016/j.jpaa.2009.06.012

Every complex plane curve C determines a subscheme S of the $P^8$ of 3x3 matrices, whose projective normal cone (PNC) captures subtle invariants of C. In "Limits of PGL(3)-translates of plane curves, I" we obtain a set-theoretic description of the PNC and thereby we determine all possible limits of families of plane curves whose general element is isomorphic to C. The main result of this article is the determination of the PNC as a cycle; this is an essential ingredient in our computation in "Linear orbits of arbitrary plane curves" of the degree of the PGL(3)-orbit closure of an arbitrary plane curve, an invariant of natural enumerative significance.

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