{"title":"Rigidity of rationally connected smooth projective varieties from dynamical viewpoints","authors":"Sheng Meng, Guolei Zhong","doi":"10.4310/mrl.2023.v30.n2.a10","DOIUrl":null,"url":null,"abstract":"Let $X$ be a rationally connected smooth projective variety of dimension $n$. We show that $X$ is a toric variety if and only if $X$ admits an int-amplified endomorphism with totally invariant ramification divisor. We also show that $X\\cong (\\mathbb{P}^1)^{\\times n}$ if and only if $X$ admits a surjective endomorphism $f$ such that the eigenvalues of $f^*|_{\\text{N}^1(X)}$ (without counting multiplicities) are $n$ distinct real numbers greater than $1$.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"190 1","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Research Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/mrl.2023.v30.n2.a10","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 8
Abstract
Let $X$ be a rationally connected smooth projective variety of dimension $n$. We show that $X$ is a toric variety if and only if $X$ admits an int-amplified endomorphism with totally invariant ramification divisor. We also show that $X\cong (\mathbb{P}^1)^{\times n}$ if and only if $X$ admits a surjective endomorphism $f$ such that the eigenvalues of $f^*|_{\text{N}^1(X)}$ (without counting multiplicities) are $n$ distinct real numbers greater than $1$.
期刊介绍:
Dedicated to publication of complete and important papers of original research in all areas of mathematics. Expository papers and research announcements of exceptional interest are also occasionally published. High standards are applied in evaluating submissions; the entire editorial board must approve the acceptance of any paper.