关于形式可识别性的一种几何方法
On a geometric method for the identifiability of forms
摘要：
我们引入了一个新的标准，测试如果一个给定的三元形式$T$的偶数度的分解是唯一的。该标准是基于分析的希尔伯特函数的投影集的点$Z$相关的分解，并在Terracini引理描述切空间割线品种。该准则在分解长度的范围内起作用，该范围等同于重塑的Kruskal准则（见[1]）起作用的范围。我们的标准确定了一个算法的可识别性的$T$这是明智的速度比算法的基础上重塑Kruskal的标准，特别是当一组点$Z$是不是在一般的位置。
英文摘要：
We introduce a new criterion which tests if a given decomposition of a given ternary form $T$ of even degree is unique. The criterion is based on the analysis of the Hilbert function of the projective set of points $Z$ associated to the decomposition, and on the Terracini's Lemma which describes tangent spaces to secant varieties. The criterion works in a range for the length of the decomposition which is equivalent to the range in which the reshaped Kruskal's criterion (see [1]) works. Our criterion determines an algorithm for the identifiability of $T$ which is sensibly faster than algorithms based on the reshaped Kruskal's criterion, especially when the set of points $Z$ is not in general position.
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