Limits of translates of plane curves, I,

P. Aluffi, C. Faber

We classify all possible limits of families of translates of a fixed, arbitrary complex plane curve. We do this by giving a set-theoretic description of the projective normal cone (PNC) of a subscheme, determined by the curve, of the P⁸ of 3x3 matrices. In a sequel to this paper we determine the multiplicities of the components of the PNC. The knowledge of the PNC as a cycle is essential in our computation of the degree of the PGL(3)-orbit closure of an arbitrary plane curve, performed in Linear orbits of arbitrary plane curves, Michigan Math J., 48 (2000) 1-37.

This paper together with its sequel (FSU07-16) supersede paper FSU03-08.