In this paper, we study the set of decompositions of symmetric tensors of low rank of any dimension and of arbitrary order and the Waring loci of points which appear in a decomposition of the tensor. We describe a new and complete stratification of the set of symmetric tensors of rank less than 5 by studying Hilbert function and regularity of ideals of points contained in the apolar ideal. For each stratum, we describe a procedure to compute a minimal apolar set of points, exploiting the algebraic properties of the Waring loci.
On minimal decompositions of low rank symmetric tensors / Mourrain, B.; Oneto, A.. - In: LINEAR ALGEBRA AND ITS APPLICATIONS. - ISSN 0024-3795. - 607:(2020), pp. 347-377. [10.1016/j.laa.2020.06.029]
On minimal decompositions of low rank symmetric tensors
Oneto A.
2020-01-01
Abstract
In this paper, we study the set of decompositions of symmetric tensors of low rank of any dimension and of arbitrary order and the Waring loci of points which appear in a decomposition of the tensor. We describe a new and complete stratification of the set of symmetric tensors of rank less than 5 by studying Hilbert function and regularity of ideals of points contained in the apolar ideal. For each stratum, we describe a procedure to compute a minimal apolar set of points, exploiting the algebraic properties of the Waring loci.| File | Dimensione | Formato | |
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