Linear degenerations of Schubert varieties

TL;DR

This paper introduces a new way to study Schubert varieties by defining linear degenerations through quiver Grassmannians, providing explicit parametrizations of orbit structures and their partial order relations.

Contribution

It develops a novel framework for linear degenerations of Schubert varieties using quiver Grassmannians and describes explicit parametrizations of orbit actions.

Findings

Explicit parametrizations of orbit actions

Description of partial order relations on orbits

New geometric perspective on degenerations

Abstract

We define linear degenerations of Schubert varieties via a special class of quiver Grassmannians. To do so, we restrict our study to an appropriate subvariety in the variety of representations of the considered quiver and describe a base change action on this subvariety. We provide two explicit parametrisations for the orbits of this action, one of which encodes the partial order relations on such orbits.