Universality of High-Strength Tensors

Author:

Bik Arthur,Danelon Alessandro,Draisma JanORCID,Eggermont Rob H.

Abstract

AbstractA theorem due to Kazhdan and Ziegler implies that, by substituting linear forms for its variables, a homogeneous polynomial of sufficiently high strength specialises to any given polynomial of the same degree in a bounded number of variables. Using entirely different techniques, we extend this theorem to arbitrary polynomial functors. As a corollary of our work, we show that specialisation induces a quasi-order on elements in polynomial functors, and that among the elements with a dense orbit there are unique smallest and largest equivalence classes in this quasi-order.

Funder

Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Universität Bern

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Reference21 articles.

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3. Ballico, E., Bik, A., Oneto, A., Ventura, E.: The set of forms with bounded strength is not closed. arXiv:2012.01237 (2020)

4. Ballico, E., Bik, A., Oneto, A., Ventura, E.: Strength and slice rank of forms are generically equal. arXiv:2102.11549 (2021)

5. Ballico, E., Ventura, E.: The strength for line bundles. Math. Scand. To appear (2020)

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The Geometry of Polynomial Representations;International Mathematics Research Notices;2022-08-18

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