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Transactions of the American Mathematical Society

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On generic identifiability of symmetric tensors of subgeneric rank


Authors: Luca Chiantini, Giorgio Ottaviani and Nick Vannieuwenhoven
Journal: Trans. Amer. Math. Soc. 369 (2017), 4021-4042
MSC (2010): Primary 14C20, 14N05, 14Q15, 15A69, 15A72
DOI: https://doi.org/10.1090/tran/6762
Published electronically: November 8, 2016
MathSciNet review: 3624400
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Abstract: 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 $ d\ge 4$ we rely on known results on weak defectivity by Ballico, Ciliberto, Chiantini, and Mella.


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Additional Information

Luca Chiantini
Affiliation: Dipartimento di Ingegneria dell’Informazione e Scienze Matematiche, Università di Siena, 53100 Siena SI, Italy
Email: luca.chiantini@unisi.it

Giorgio Ottaviani
Affiliation: Dipartimento di Matematica e Informatica “Ulisse Dini”, Università di Firenze, 50134 Firenze, Italy
Email: ottavian@math.unifi.it

Nick Vannieuwenhoven
Affiliation: Department of Computer Science, KU Leuven, B-3001 Leuven-Heverlee, Belgium
Email: nick.vannieuwenhoven@cs.kuleuven.be

DOI: https://doi.org/10.1090/tran/6762
Received by editor(s): April 27, 2015
Received by editor(s) in revised form: June 1, 2015
Published electronically: November 8, 2016
Additional Notes: The first and second authors are members of the Italian GNSAGA-INDAM
The third author was supported by a Ph.D. fellowship of the Research Foundation–Flanders (FWO)
Article copyright: © Copyright 2016 American Mathematical Society

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