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arXiv · 1212.6338

An analogue of Bott's theorem for Schubert varieties-related to torus semistable points

S. Senthamarai Kannan
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Abstract

Let $G$ be a simple, simply connected algebraic group over the field of complex numbers. We give a necessary and a sufficient condition for a Schubert variety $X(τ)$ for which all the higher cohomologies $H^{i}(X(τ), E)$ vanish for the restriction $E$ of the tangent bundle of $G/B$ to X(τ)$. We further show that the global sections $H^{0}(X(τ), E)$ is the adjoint representation of $G$ when $G$ is simply laced.

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S. Senthamarai Kannan. 2013-03-01. An analogue of Bott's theorem for Schubert varieties-related to torus semistable points. https://arxiv.org/abs/1212.6338

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