Symmetric powers: structure, smoothability, and applications
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908508903964672 |
|---|---|
| author | Flavi, Cosimo Jelisiejew, Joachim Michałek, Mateusz |
| author_facet | Flavi, Cosimo Jelisiejew, Joachim Michałek, Mateusz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02754 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetric powers: structure, smoothability, and applications Flavi, Cosimo Jelisiejew, Joachim Michałek, Mateusz Algebraic Geometry Computational Complexity Commutative Algebra 15A69, 14N07, 68Q15, 13D10 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. |
| title | Symmetric powers: structure, smoothability, and applications |
| topic | Algebraic Geometry Computational Complexity Commutative Algebra 15A69, 14N07, 68Q15, 13D10 |
| url | https://arxiv.org/abs/2408.02754 |