Grassmann流形正则爆破的一个消失定理

IF 0.5 Q3 MATHEMATICS Complex Manifolds Pub Date : 2021-01-01 DOI:10.1515/coma-2020-0126

Hanlong Fang, Song-Chun Zhu

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引用次数: 1

摘要

设，p,n是由与参数s相关的pl cker坐标子空间的吹胀构造的Grassmann流形G(p, n)的正则吹胀。我们证明了，p,n的切束的高上同群消失。作为应用，𝒯s,p,n在Kodaira-Spencer意义上是局部刚性的。

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A vanishing theorem for the canonical blow-ups of Grassmann manifolds

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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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： 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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