### Abstract

*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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*European Journal of Mathematics*,

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

**Reconstructing toric quiver flag varieties from a tilting bundle.** / Craw, Alastair; Green, James.

Research output: Contribution to journal › Article

*European Journal of Mathematics*, vol. 4, no. 1, pp. 185–199. https://doi.org/10.1007/s40879-017-0194-9

}

TY - JOUR

T1 - Reconstructing toric quiver flag varieties from a tilting bundle

AU - Craw, Alastair

AU - Green, James

PY - 2018/3/1

Y1 - 2018/3/1

N2 - 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 $\bigoplus_{0\leq i\leq n} \mathcal{O}_{\mathbb{P}^n}(i)$.

AB - 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 $\bigoplus_{0\leq i\leq n} \mathcal{O}_{\mathbb{P}^n}(i)$.

KW - Moduli spaces of quiver representations

KW - Multigraded linear series

KW - Tilting bundles

UR - http://www.scopus.com/inward/record.url?scp=85042733232&partnerID=8YFLogxK

U2 - 10.1007/s40879-017-0194-9

DO - 10.1007/s40879-017-0194-9

M3 - Article

VL - 4

SP - 185

EP - 199

JO - European Journal of Mathematics

JF - European Journal of Mathematics

SN - 2199-675X

IS - 1

ER -