{"title":"格拉斯曼之间的变形，II","authors":"Gianluca Occhetta, Eugenia Tondelli","doi":"10.1007/s00013-024-01986-y","DOIUrl":null,"url":null,"abstract":"<div><p>Denote by <span>\\({\\mathbb {G}}(k,n)\\)</span> the Grassmannian of linear subspaces of dimension <i>k</i> in <span>\\({\\mathbb {P}}^n\\)</span>. We show that if <span>\\(\\varphi :{\\mathbb {G}}(l,n) \\rightarrow {\\mathbb {G}}(k,n)\\)</span> is a nonconstant morphism and <span>\\(l \\not =0,n-1\\)</span>, then <span>\\(l=k\\)</span> or <span>\\(l=n-k-1\\)</span> and <span>\\(\\varphi \\)</span> is an isomorphism.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-01986-y.pdf","citationCount":"0","resultStr":"{\"title\":\"Morphisms between Grassmannians, II\",\"authors\":\"Gianluca Occhetta, Eugenia Tondelli\",\"doi\":\"10.1007/s00013-024-01986-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Denote by <span>\\\\({\\\\mathbb {G}}(k,n)\\\\)</span> the Grassmannian of linear subspaces of dimension <i>k</i> in <span>\\\\({\\\\mathbb {P}}^n\\\\)</span>. We show that if <span>\\\\(\\\\varphi :{\\\\mathbb {G}}(l,n) \\\\rightarrow {\\\\mathbb {G}}(k,n)\\\\)</span> is a nonconstant morphism and <span>\\\\(l \\\\not =0,n-1\\\\)</span>, then <span>\\\\(l=k\\\\)</span> or <span>\\\\(l=n-k-1\\\\)</span> and <span>\\\\(\\\\varphi \\\\)</span> is an isomorphism.</p></div>\",\"PeriodicalId\":8346,\"journal\":{\"name\":\"Archiv der Mathematik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-03-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00013-024-01986-y.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archiv der Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00013-024-01986-y\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archiv der Mathematik","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00013-024-01986-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
Abstract Denote by \({\mathbb {G}}(k,n)\) the Grassmannian of linear subspaces of dimension k in \({\mathbb {P}}^n\) .我们证明如果 \(\varphi :{\mathbb {G}}(l,n) \rightarrow {\mathbb {G}}(k,n)\) 是一个非恒定变形并且 \(l \not =0,n-1\) ，那么 \(l=k\) 或者 \(l=n-k-1\) 和 \(\varphi\) 是一个同构。
Denote by \({\mathbb {G}}(k,n)\) the Grassmannian of linear subspaces of dimension k in \({\mathbb {P}}^n\). We show that if \(\varphi :{\mathbb {G}}(l,n) \rightarrow {\mathbb {G}}(k,n)\) is a nonconstant morphism and \(l \not =0,n-1\), then \(l=k\) or \(l=n-k-1\) and \(\varphi \) is an isomorphism.
期刊介绍：
Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.
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