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

作者：Aluffi Paolo^*; Faber Carel

来源：Journal of Pure and Applied Algebra, 2010, 214(5): 526-547.

DOI：10.1016/j.jpaa.2009.06.010

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(8) of 3 x 3 matrices to the P(N) 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 [P. Aluffi, C. Faber, Linear orbits of arbitrary plane curves, Michigan Math. J. 48(2000) 1-37].

• 出版日期2010-5