Reconstructing toric quiver flag varieties from a tilting bundle

Abstract

We prove that every toric quiver flag variety $Y$ is isomorphic to a fine moduli space of cyclic modules over the algebra $\text{End}(T)$ for some tilting bundle $T$ on $Y$. This generalises the well known fact that ${\mathbb{P}}^n$ can be recovered from the endomorphism algebra of ${⨁}_{0\le i\le n}{\mathcal{O}}_{{\mathbb{P}}^n}(i)$.

12 pages, final version