Stability of restrictions of cotangent bundles of hypersurfaces
Résumé
Let $Y\subset\mathbb{P}^{n+1}$ be a general smooth hypersurface of dimension $\geq 3$. It is well-known that the cotangent bundle $\Omega_Y^1$ is stable. In this note, we prove that the restriction $\Omega_Y^1|_X$ over a general smooth hypersurface $X$ of $Y$ with $Pic(Y)\cong Pic(X)$ is stable except for some well-known examples. We also address the cases where the Picard group increases by restriction.