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arXiv · 2108.11069

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

Hanlong Fang·Songhao Zhu
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Abstract

Let $\mathcal T_{s,p,n}$ be the canonical blow-up of the Grassmann manifold $G(p,n)$ constructed by blowing up the Pl\"ucker 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.

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Hanlong Fang, Songhao Zhu. 2021-08-25. A vanishing theorem for the canonical blow-ups of Grassmann manifolds. https://arxiv.org/abs/2108.11069

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