论文标题
关于形式可识别性的几何方法
On a geometric method for the identifiability of forms
论文作者
论文摘要
我们引入了一个新标准，该标准测试是否给定三元形式的$ t $均匀度的给定分解是独一无二的。该标准是基于对与分解相关的点$ z $的希尔伯特功能的分析，以及在Terracini的引理上描述了切线品种的切线空间。该标准在分解长度的范围内起作用，这与重塑Kruskal标准（见[1]）的范围相当。我们的标准确定了$ t $可识别性的算法，该算法比基于重塑的Kruskal标准要快的速度要快，尤其是当点$ z $不在一般位置时。
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.
