ON GENERIC IDENTIFIABILITY OF SYMMETRIC TENSORS OF SUBGENERIC RANK

被引：62

作者：

Chiantini, Luca ^{[1
]}

Ottaviani, Giorgio ^{[2
]}

Vannieuwenhoven, Nick ^{[3
]}

机构：

[1] Univ Siena, Dipartimento Ingn Informaz & Sci Matemat, I-53100 Siena, SI, Italy

[2] Univ Florence, Dipartimento Matemat & Informat Ulisse Dini, I-50134 Florence, Italy

[3] Katholieke Univ Leuven, Dept Comp Sci, B-3001 Leuven Heverlee, Belgium

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 369卷 / 06期

关键词：

SECANT VARIETIES; LINEAR-SYSTEMS; UNIQUENESS; DECOMPOSITIONS;

D O I：

10.1090/tran/6762

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the general symmetric tensor in (SCn)-C-d+(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 d >= 4 we rely on known results on weak defectivity by Ballico, Ciliberto, Chiantini, and Mella.

引用

页码：4021 / 4042

页数：22

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