Cosimo Flavi, Joachim Jelisiejew, Mateusz Michałek
{"title":"Symmetric powers: structure, smoothability, and applications","authors":"Cosimo Flavi, Joachim Jelisiejew, Mateusz Michałek","doi":"arxiv-2408.02754","DOIUrl":null,"url":null,"abstract":"We investigate border ranks of twisted powers of polynomials and\nsmoothability of symmetric powers of algebras. We prove that the latter are\nsmoothable. For the former, we obtain upper bounds for the border rank in\ngeneral and prove that they are optimal under mild conditions. We give\napplications to complexity theory.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Commutative Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.02754","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.
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