Unitary grassmannians

TL;DR

This paper investigates the properties of projective homogeneous varieties under unitary group actions, focusing on grassmannians of isotropic subspaces of hermitian forms, establishing their 2-incompressibility in generic cases.

Contribution

It proves that unitary grassmannians of totally isotropic subspaces are 2-incompressible when the hermitian form is generic, with applications to orthogonal grassmannians.

Findings

Unitary grassmannians are 2-incompressible for generic hermitian forms.

Provides new insights into the structure of projective homogeneous varieties under unitary groups.

Applications extend to orthogonal grassmannians.

Abstract

We study projective homogeneous varieties under an action of a projective unitary group (of outer type). We are especially interested in the case of (unitary) grassmannians of totally isotropic subspaces of a hermitian form over a field, the main result saying that these grassmannians are 2-incompressible if the hermitian form is generic. Applications to orthogonal grassmannians are provided.