{"title":"二次元上均匀束的分裂","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":"8 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":\"8 1\",\"pages\":\"\"},\"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}","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}
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