Countably many asymptotic tensor ranks
Algebraic Geometry
2022-12-26 v1 Computational Complexity
Abstract
In connection with recent work on gaps in the asymptotic subranks of complex tensors the question arose whether the number of nonnegative real numbers that arise as the asymptotic subrank of some complex tensor is countable. In this short note we settle this question in the affirmative, for all tensor invariants that are algebraic in the sense that they are invariant under field automorphisms of the complex numbers.
Keywords
Cite
@article{arxiv.2212.12219,
title = {Countably many asymptotic tensor ranks},
author = {Andreas Blatter and Jan Draisma and Filip Rupniewski},
journal= {arXiv preprint arXiv:2212.12219},
year = {2022}
}