Quasi-projective varieties are Grassmannians for fully exact subcategories of quiver representations

TL;DR

This paper demonstrates that quasi-projective varieties can be realized as Grassmannians within fully exact subcategories of quiver representations, extending Reineke's isomorphism results.

Contribution

It introduces a restriction of Reineke's isomorphism to Grassmannians for fully exact subcategories, establishing a new connection between varieties and quiver Grassmannians.

Findings

Quasi-projective varieties are isomorphic to Grassmannians in certain subcategories.

Extension of Reineke's isomorphism to fully exact subcategories.

New framework for realizing varieties as quiver Grassmannians.

Abstract

Reineke and independent other authors proved that every projective variety arises as a quiver Grassmannian. We prove the claim in the title by restricting Reineke's isomorphism to Grassmannians for a fully exact subcategory.