Limits of translates of plane curves, II

P. Aluffi, C. Faber

Every complex plane curve C determines a subscheme S of the P⁸ of 3x3 matrices, whose projective normal cone (PNC) captures subtle invariants of C.

In a previous paper (FSU07-15) 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, Michigan Math J., 48 (2000) 1-37, of the degree of the PGL(3)-orbit closure of an arbitrary plane curve, an invariant of natural enumerative significance.

This paper, together with FSU07-15, supersede paper FSU03-08.