# Reconstructing toric quiver flag varieties from a tilting bundle

Alastair Craw, James Green

Research output: Contribution to journalArticle

### Abstract

We prove that every toric quiver flag variety Y is isomorphic to a fine moduli space of cyclic modules over the algebra 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 $\bigoplus_{0\leq i\leq n} \mathcal{O}_{\mathbb{P}^n}(i)$.
Original language English 185–199 15 European Journal of Mathematics 4 1 7 Nov 2017 https://doi.org/10.1007/s40879-017-0194-9 Published - 1 Mar 2018

Flag Variety
Tilting
Quiver
Bundle
Algebra
Endomorphism
Moduli Space
Isomorphic
Module
Generalise

### Keywords

• Moduli spaces of quiver representations
• Tilting bundles

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

In: European Journal of Mathematics, Vol. 4, No. 1, 01.03.2018, p. 185–199.

Research output: Contribution to journalArticle

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