{"title":"Isolated torus invariants and automorphism groups of rigid varieties","authors":"Viktoriia Borovik , Sergey Gaifullin","doi":"10.1016/j.jalgebra.2024.12.009","DOIUrl":null,"url":null,"abstract":"<div><div>Perepechko and Zaidenberg conjectured that the neutral component of the automorphism group of a rigid affine variety is a torus. We prove this conjecture for toric varieties and varieties with a torus action of complexity one. We also obtain a criterion for an <em>m</em>-suspension over a rigid variety to be rigid (for every rigid variety and every regular function). Additionally, we study the automorphism group of <em>m</em>-suspensions satisfying this criterion.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"666 ","pages":"Pages 821-839"},"PeriodicalIF":0.8000,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869324006756","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Perepechko and Zaidenberg conjectured that the neutral component of the automorphism group of a rigid affine variety is a torus. We prove this conjecture for toric varieties and varieties with a torus action of complexity one. We also obtain a criterion for an m-suspension over a rigid variety to be rigid (for every rigid variety and every regular function). Additionally, we study the automorphism group of m-suspensions satisfying this criterion.
期刊介绍：
The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.
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