The Rigidity Problem in Orthogonal Grassmannians

TL;DR

This paper classifies rigid Schubert classes in orthogonal Grassmannians and provides combinatorial conditions ensuring certain linear spaces meet fixed spaces in the expected dimension.

Contribution

It offers a classification of rigidity for Schubert classes and introduces combinatorial criteria for intersection properties in orthogonal Grassmannians.

Findings

Identified all rigid Schubert classes in orthogonal Grassmannians.

Developed combinatorial conditions for linear space intersections.

Provided a framework for understanding rigidity in these geometric contexts.

Abstract

We classify rigid Schubert classes in orthogonal Grassmannians. More generally, given a representative $X$ of a Schubert class in an orthogonal Grassmannian, we give combinatorial conditions which guarantee that every linear space parametrized by $X$ meets a fixed linear space in the required dimension.