{"title":"A vanishing theorem for the canonical blow-ups of Grassmann manifolds","authors":"Hanlong Fang, Song-Chun Zhu","doi":"10.1515/coma-2020-0126","DOIUrl":null,"url":null,"abstract":"Abstract Let 𝒯 s,p,n be the canonical blow-up of the Grassmann manifold G(p, n) constructed by blowing up the Plücker coordinate subspaces associated with the parameter s. We prove that the higher cohomology groups of the tangent bundle of 𝒯 s,p,n vanish. As an application, 𝒯s,p,n is locally rigid in the sense of Kodaira-Spencer.","PeriodicalId":42393,"journal":{"name":"Complex Manifolds","volume":"8 1","pages":"415 - 439"},"PeriodicalIF":0.5000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Complex Manifolds","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/coma-2020-0126","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract Let 𝒯 s,p,n be the canonical blow-up of the Grassmann manifold G(p, n) constructed by blowing up the Plücker coordinate subspaces associated with the parameter s. We prove that the higher cohomology groups of the tangent bundle of 𝒯 s,p,n vanish. As an application, 𝒯s,p,n is locally rigid in the sense of Kodaira-Spencer.
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Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.
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