{"title":"论PGL(d,C)/P型抛物几何","authors":"I. Biswas","doi":"10.1215/KJM/1250271316","DOIUrl":null,"url":null,"abstract":"Let P be the maximal parabolic subgroup of PGL( d, C ) defined by invertible matrices ( a ij ) di,j =1 with a dj = 0 for all j ∈ [1 , d − 1]. Take a holomorphic parabolic geometry ( M, E P , ω ) of type PGL( d, C ) /P . Assume that M is a complex projective manifold. We prove the following: If there is a nonconstant holomorphic map f : CP 1 −→ M , then M is biholomorphic to the projective space CP d − 1 .","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"48 1","pages":"747-755"},"PeriodicalIF":0.0000,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On parabolic geometry of type PGL(d,C)/P\",\"authors\":\"I. Biswas\",\"doi\":\"10.1215/KJM/1250271316\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let P be the maximal parabolic subgroup of PGL( d, C ) defined by invertible matrices ( a ij ) di,j =1 with a dj = 0 for all j ∈ [1 , d − 1]. Take a holomorphic parabolic geometry ( M, E P , ω ) of type PGL( d, C ) /P . Assume that M is a complex projective manifold. We prove the following: If there is a nonconstant holomorphic map f : CP 1 −→ M , then M is biholomorphic to the projective space CP d − 1 .\",\"PeriodicalId\":50142,\"journal\":{\"name\":\"Journal of Mathematics of Kyoto University\",\"volume\":\"48 1\",\"pages\":\"747-755\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematics of Kyoto University\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1215/KJM/1250271316\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematics of Kyoto University","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1215/KJM/1250271316","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
摘要
设P是对所有j∈[1,d−1]由可逆矩阵(a ij) di,j =1, dj = 0定义的PGL(d, C)的极大抛物子群。取PGL(d, C) /P型全纯抛物几何(M, exp， ω)。假设M是一个复射影流形。我们证明了:如果存在一个非常全纯映射f: CP 1−→M，则M对射影空间CP d−1是生物全纯的。
Let P be the maximal parabolic subgroup of PGL( d, C ) defined by invertible matrices ( a ij ) di,j =1 with a dj = 0 for all j ∈ [1 , d − 1]. Take a holomorphic parabolic geometry ( M, E P , ω ) of type PGL( d, C ) /P . Assume that M is a complex projective manifold. We prove the following: If there is a nonconstant holomorphic map f : CP 1 −→ M , then M is biholomorphic to the projective space CP d − 1 .
期刊介绍：
Papers on pure and applied mathematics intended for publication in the Kyoto Journal of Mathematics should be written in English, French, or German. Submission of a paper acknowledges that the paper is original and is not submitted elsewhere.
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