Limits of translates of plane curves -- on a paper of Aldo Ghizzetti

P. Aluffi, C. Faber

We study the limits of $\PGL(3)$ translates of an arbitrary plane curve, giving a description of all possible limits of a given curve and computing the multiplicities of corresponding components in the normal cone to the base scheme of a related linear system. This information is a key step in the computation of the degree of the closure of the {\em linear orbit\/} of an arbitrary plane curve.

Our analysis recovers and extends results obtained by Aldo Ghizzetti in the 1930's.

This paper is superseded by FSU07-15 and FSU07-16, which streamline the exposition.