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

Abstract

Let ${\mathcal{T}}_{s,p,n}$ 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 ${\mathcal{T}}_{s,p,n}$ vanish. As an application, ${\mathcal{T}}_{s,p,n}$ is locally rigid in the sense of Kodaira-Spencer.

Comments are welcome. arXiv admin note: text overlap with arXiv:2007.06200