Stability of restrictions of cotangent bundles of irreducible Hermitian symmetric spaces of compact type

TL;DR

This paper proves the stability of the restricted cotangent bundle on certain subvarieties of Hermitian symmetric spaces, extending known stability results to broader classes of complete intersections.

Contribution

It establishes the stability of cotangent bundle restrictions for a wide class of complete intersections in Hermitian symmetric spaces, including cases with Picard group changes.

Findings

Restricted cotangent bundles are stable under specified conditions.

Stability holds for complete intersections with surjective Picard group maps.

Addresses cases with Picard group increase by restriction.

Abstract

It is known that the cotangent bundle $\Omega_Y$ of an irreducible Hermitian symmetric space $Y$ of compact type is stable. Except for a few obvious exceptions, we show that if $X \subset Y$ is a complete intersection such that $Pic(Y) \to Pic(X)$ is surjective, then the restriction $\Omega_{Y|X}$ is stable. We then address some cases where the Picard group increases by restriction.