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

Let T be the canonical blow-up of the Grassmann manifold , ) constructed by blowing up the Plücker coordinate subspaces associated with the parameter . We prove that the higher cohomology groups of the tangent bundle of T vanish. As an application, T is locally rigid in the sense of Kodaira-Spencer....

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Veröffentlicht in:	Complex manifolds (Warsaw, Poland) Poland), 2021-01, Vol.8 (1), p.415-439
Hauptverfasser:	Fang, Hanlong, Zhu, Songhao
Format:	Artikel
Sprache:	eng
Schlagworte:	14M17 32G05 cohomology of the tangent bundle locally rigid the canonical blow-ups of Grassmann manifolds
Online-Zugang:	Volltext
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Zusammenfassung:	Let T be the canonical blow-up of the Grassmann manifold , ) constructed by blowing up the Plücker coordinate subspaces associated with the parameter . We prove that the higher cohomology groups of the tangent bundle of T vanish. As an application, T is locally rigid in the sense of Kodaira-Spencer.
ISSN:	2300-7443 2300-7443
DOI:	10.1515/coma-2020-0126