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# Restriction of the Tangent Bundle of $G/P$ to a Hypersurface

Published:2009-12-04
Printed: Jun 2010
• Indranil Biswas
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## Abstract

Let P be a maximal proper parabolic subgroup of a connected simple linear algebraic group G, defined over $\mathbb C$, such that $n := \dim_{\mathbb C} G/P \geq 4$. Let $\iota \colon Z \hookrightarrow G/P$ be a reduced smooth hypersurface of degree at least $(n-1)\cdot \operatorname{degree}(T(G/P))/n$. We prove that the restriction of the tangent bundle $\iota^*TG/P$ is semistable.
 Keywords: tangent bundle, homogeneous space, semistability, hypersurface
 MSC Classifications: 14F05 - Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 14J60 - Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx] 14M15 - Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]

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