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Mathematics > Commutative Algebra

arXiv:1805.11940 (math)
[Submitted on 30 May 2018]

Title:On minimal decompositions of low rank symmetric tensors

Authors:Bernard Mourrain, Alessandro Oneto
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Abstract:We use an algebraic approach to construct minimal decompositions of symmetric tensors with low rank. This is done by using Apolarity Theory and by studying minimal sets of reduced points apolar to a given symmetric tensor, namely, whose ideal is contained in the apolar ideal associated to the tensor. In particular, we focus on the structure of the Hilbert function of these ideals of points. We give a procedure which produces a minimal set of points apolar to any symmetric tensor of rank at most 5. This procedure is also implemented in the algebra software Macaulay2.
Comments: 26 pages; the Macaulay2 package "ApolarLowRank.m2" is available in the ancillary files
Subjects: Commutative Algebra (math.AC); Algebraic Geometry (math.AG)
MSC classes: 13P05, 14N20, 13F20, 14N05
Cite as: arXiv:1805.11940 [math.AC]
  (or arXiv:1805.11940v1 [math.AC] for this version)
  https://doi.org/10.48550/arXiv.1805.11940

Submission history

From: Alessandro Oneto [view email]
[v1] Wed, 30 May 2018 13:29:19 UTC (1,184 KB)
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