On generic identifiability of symmetric tensors of subgeneric rank
On generic identifiability of symmetric tensors of subgeneric rank
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亚泛阶对称张量的泛可辨性
DOI：
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发表时间：
2015
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通讯作者：
N. Vannieuwenhoven
中科院分区：
文献类型：
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作者：
L. Chiantini;G. Ottaviani;N. Vannieuwenhoven
证明了秩为r的$S^d {mathbb C}^{n+1}$中的一般对称张量是可识别的，只要r小于一般秩。也就是说，它作为线性形式的r次幂和的沃林分解是唯一的。只有三个例外情况出现，所有这些都是已知的文献。我们最初的贡献是考虑立方体（d=3）的情况，而对于dge 4，我们依赖于balico， Ciliberto， Chiantini和Mella关于弱缺陷的已知结果。
We prove that the general symmetric tensor in $S^d {mathbb C}^{n+1}$ of rank r is identifiable, provided that r is smaller than the generic rank. That is, its Waring decomposition as a sum of r powers of linear forms is unique. Only three exceptional cases arise, all of which were known in the literature. Our original contribution regards the case of cubics ($d=3$), while for $dge 4$ we rely on known results on weak defectivity by Ballico, Ciliberto, Chiantini, and Mella.