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

http://dx.doi.org/10.4153/CMB-2010-005-1
Canad. Math. Bull. 53(2010), 218-222

  Published:2009-12-04
 Printed: Jun 2010

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.