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

It is known that the cotangent bundle ΩY of an irreducible Hermitian symmetric space Y of compact type is stable. We show that if X ⊂ Y is a subvariety whose structure sheaf has a short split resolution and such that the restriction map Pic(Y ) → Pic(X) is surjective, then, apart from a few exceptions, the restriction ΩY∣X is a stable bundle. We then address some cases where the Picard group increases by restriction. [ABSTRACT FROM AUTHOR]