Polynomials and tensors of bounded strength

Bik, Arthur; Draisma, Jan; Eggermont, Rob H. (2019). Polynomials and tensors of bounded strength. Commununications in contemporary mathematics, 21(7), p. 1850062. World Scientific 10.1142/S0219199718500621

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Notions of rank abound in the literature on tensor decomposition. We prove that strength, recently introduced for homogeneous polynomials by Ananyan–Hochster in their proof of Stillman’s conjecture and generalized here to other tensors, is universal among these ranks in the following sense: any non-trivial Zariski-closed condition on tensors that is functorial in the underlying vector space implies bounded strength. This generalizes a theorem by Derksen–Eggermont–Snowden on cubic polynomials, as well as a theorem by Kazhdan–Ziegler which says that a polynomial all of whose directional derivatives have bounded strength must itself have bounded strength.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Bik, Michel Arthur and Draisma, Jan

Subjects:

500 Science > 510 Mathematics

ISSN:

0219-1997

Publisher:

World Scientific

Language:

English

Submitter:

Michel Arthur Bik

Date Deposited:

14 Oct 2019 13:09

Last Modified:

23 Oct 2019 13:12

Publisher DOI:

10.1142/S0219199718500621

ArXiv ID:

1805.01816

BORIS DOI:

10.7892/boris.133872

URI:

https://boris.unibe.ch/id/eprint/133872

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