Schubert Quiver Grassmannians

TL;DR

This paper studies a class of quiver Grassmannians, showing they are composed of Schubert varieties, and provides explicit descriptions and computations of their geometric properties.

Contribution

It introduces a new class of quiver Grassmannians generalizing degenerate flag varieties and characterizes their irreducible components as Schubert varieties.

Findings

Each irreducible component is isomorphic to a Schubert variety

Explicit description of irreducible components

Computed Poincaré polynomials of the quiver Grassmannians

Abstract

Quiver Grassmannians are projective varieties parametrizing subrepresentations of given dimension in a quiver representation. We define a class of quiver Grassmannians generalizing those which realize degenerate flag varieties. We show that each irreducible component of the quiver Grassmannians in question is isomorphic to a Schubert variety. We give an explicit description of the set of irreducible components, identify all the Schubert varieties arising, and compute the Poincar\'e polynomials of these quiver Grassmannians.