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Mathematics > Algebraic Geometry

arXiv:0706.1301 (math)
[Submitted on 9 Jun 2007 (v1), last revised 6 Jun 2009 (this version, v4)]

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

Authors:Paolo Aluffi, Carel Faber
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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 $P^8$ of 3x3 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 our earlier paper "Linear orbits of arbitrary plane curves".
Comments: 28 pages. Minor revision. Final version
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14E05, 14H50, 14L35, 14N10
Cite as: arXiv:0706.1301 [math.AG]
  (or arXiv:0706.1301v4 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.0706.1301
Journal reference: J. Pure Appl. Algebra 214 (2010), no. 5, 526-547
Related DOI: https://doi.org/10.1016/j.jpaa.2009.06.010

Submission history

From: Carel Faber [view email]
[v1] Sat, 9 Jun 2007 11:21:06 UTC (40 KB)
[v2] Mon, 16 Jul 2007 13:07:37 UTC (52 KB)
[v3] Thu, 5 Feb 2009 00:38:27 UTC (63 KB)
[v4] Sat, 6 Jun 2009 20:36:54 UTC (104 KB)
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