Stability of Restrictions of the Cotangent Bundle of Irreducible Hermitian Symmetric Spaces of Compact Type

Abstract

It is known that the cotangent bundle $\Omega\_Y$ of an irreducible Hermitian symmetric space $Y$ of compact type is stable. We show that if $X \subset Y$ is a subvariety whose structure sheaf has a short split resolution and such that the restriction map Pic$(Y) \to$ Pic$(X)$ is surjective, then, apart from a few exceptions, the restriction $\Omega\_{Y|X}$ is a stable bundle. We then address some cases where the Picard group increases by restriction.