On the rigidity of admissible pairs of rational homogeneous spaces of Picard number one which are of deletion type

TL;DR

This paper investigates the rigidity of certain pairs of rational homogeneous spaces of Picard number one, focusing on deletion type, and provides examples demonstrating rigidity under rational saturation conditions.

Contribution

It offers new examples of rigid admissible pairs of deletion type spaces using Mok's theorem and the concept of rational saturation.

Findings

Examples of rigid admissible pairs of deletion type spaces are provided.

Rigidity holds under the assumption of rational saturation for these pairs.

The paper extends understanding of rigidity beyond subdiagram type cases.

Abstract

The notion of admissible pairs of rational homogeneous spaces of Picard number one and their rigidity in terms of the geometric substructures was formulated by Mok and Zhang. The rigidity is known for subdiagram type. While when the admissible pair is of deletion type, the rigidity no longer holds and we need additional conditions. Mok gave a general criterion to handle the admissible pairs which are not of subdiagram type. In this short note we give some examples of admissible pairs of irreducible compact Hermitian symmetric spaces of deletion type to be rigid under the assumption of rational saturation, as an application of Mok's theorem.