J un 2 00 9 LIMITS OF PGL ( 3 ) - TRANSLATES OF PLANE CURVES , I

Abstract

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 the base scheme of a natural rational map, determined by the curve, from the P of 3 × 3 matrices to the P of plane curves of degree d. 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 [5].

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Cite this paper

@inproceedings{Aluffi2009JU2, title={J un 2 00 9 LIMITS OF PGL ( 3 ) - TRANSLATES OF PLANE CURVES , I}, author={Paolo Aluffi and Carel Faber}, year={2009} }