From brick manifolds to Grassmannians of bimodules

TL;DR

This paper explores Grassmannians of sub-bimodules over quiver path algebras, connecting brick manifolds and quiver representation spaces, and provides explicit constructions, smoothness proofs, cellular decompositions, and motive formulas.

Contribution

It introduces explicit constructions and smoothness results for Grassmannians of sub-bimodules, linking brick manifolds with quiver representation spaces and framed moduli spaces.

Findings

Proved smoothness of the Grassmannians

Constructed cellular decompositions

Derived recursive motive formulas

Abstract

We study a class of Grassmannians of sub-bimodules over the path algebras of quivers. Our quiver Grassmannians include Escobar's brick manifolds as well as Labelle's generalizations. We give an explicit construction of the varieties in question, provide examples and clarify connection with the quiver representation spaces. We also prove smoothness of our Grassmannians, construct cellular decompositions and derive a realization as framed moduli spaces. The framed moduli realization leads to a recursive formula for the motives.