### Abstract

We prove that every toric quiver flag variety

*Y*is isomorphic to a fine moduli space of cyclic modules over the algebra**End**(*) for some tilting bundle***T***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 |
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Pages (from-to) | 185–199 |

Number of pages | 15 |

Journal | European Journal of Mathematics |

Volume | 4 |

Issue number | 1 |

Early online date | 7 Nov 2017 |

DOIs | |

Publication status | Published - 1 Mar 2018 |

### Keywords

- Moduli spaces of quiver representations
- Multigraded linear series
- Tilting bundles

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Craw, A., & Green, J. (2018). Reconstructing toric quiver flag varieties from a tilting bundle.

*European Journal of Mathematics*,*4*(1), 185–199. https://doi.org/10.1007/s40879-017-0194-9