Symmetric powers: structure, smoothability, and applications
Algebraic Geometry
2025-09-01 v2 Computational Complexity
Commutative Algebra
Abstract
We investigate border ranks of twisted powers of polynomials and smoothability of symmetric powers of algebras. We prove that the latter are smoothable. For the former, we obtain upper bounds for the border rank in general and prove that they are optimal under mild conditions. We give applications to complexity theory. Many of the results rest on the notion of an encompassing polynomial, which we introduce.
Cite
@article{arxiv.2408.02754,
title = {Symmetric powers: structure, smoothability, and applications},
author = {Cosimo Flavi and Joachim Jelisiejew and Mateusz Michałek},
journal= {arXiv preprint arXiv:2408.02754},
year = {2025}
}
Comments
v2, final