{"title":"Splitting of uniform bundles on quadrics","authors":"Xinyi Fang, Duo Li, Yanjie Li","doi":"arxiv-2409.02365","DOIUrl":null,"url":null,"abstract":"We show that there exist only constant morphisms from\n$\\mathbb{Q}^{2n+1}(n\\geq 1)$ to $\\mathbb{G}(l,2n+1)$ if $l$ is even $(0<l<2n)$\nand $(l,2n+1)$ is not $ (2,5)$. As an application, we prove on\n$\\mathbb{Q}^{2m+1}$ and $\\mathbb{Q}^{2m+2}(m\\geq 3)$, any uniform bundle of\nrank $2m$ splits.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.02365","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 show that there exist only constant morphisms from
$\mathbb{Q}^{2n+1}(n\geq 1)$ to $\mathbb{G}(l,2n+1)$ if $l$ is even $(0