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.