Closures of K-orbits in the flag variety for U(p,q)

TL;DR

This paper classifies certain orbits in the flag variety for GL_{p+q}, identifying those with rationally smooth closure and showing they are either closed or derived from smooth orbits in partial flag varieties.

Contribution

It provides a complete classification of GL_p x GL_q-orbits with rationally smooth closure in the flag variety, linking them to smooth orbits in partial flag varieties.

Findings

All rationally smooth closed orbits are either already closed or pullbacks from smooth partial flag variety orbits.

The classification clarifies the structure of orbits with rational smoothness in the flag variety.

The results connect orbit closures with geometric smoothness properties.

Abstract

We classify the GL_p x GL_q-orbits in the flag variety for GL_{p+q} with rationally smooth closure, showing that they are all either already closed or are pullbacks from orbits with smooth closure in a partial flag variety.