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摘要翻译：
我们对固定任意复平面曲线平移族的所有可能极限进行了分类。我们给出了自然有理映射的基格式的射影法锥(PNC)的集合论描述，它是由曲线决定的，从3×3矩阵的$P^8$到D$次平面曲线的$P^n$。在本文的续篇中，我们确定了PNC的分量的多重性。PNC作为圈的知识在我们计算任意平面曲线的PGL(3)-轨道闭包度时是必不可少的，在我们以前的论文“任意平面曲线的线性轨道”中进行了计算。
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英文标题：
《Limits of PGL(3)-translates of plane curves, I》
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作者：
Paolo Aluffi, Carel Faber
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最新提交年份：
2009
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
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".
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PDF链接：
https://arxiv.org/pdf/0706.1301
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