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

Every complex plane curve CC determines a subscheme SS of the P8P8 of 3×3 matrices, whose projective normal cone   (PNC) captures subtle invariants of CC.In [P. Aluffi, C. Faber, Limits of PGL(3)-translates of plane curves, I, J. Pure Appl. Algebra 214 (5) (2010) 526–547] 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 CC. The main result of this article is the determination of the PNC as a cycle  ; this is an essential ingredient in our computation in [P. Aluffi, C. Faber, Linear orbits of arbitrary plane curves, Michigan Math. J. 48 (2000) 1–37] of the degree of the PGL(3)PGL(3)-orbit closure of an arbitrary plane curve, an invariant of natural enumerative significance.