Reconstructing toric quiver flag varieties from a tilting bundle

Alastair Craw, James Green

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)185–199
Number of pages15
JournalEuropean Journal of Mathematics
Issue number1
Early online date7 Nov 2017
Publication statusPublished - 1 Mar 2018


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

ASJC Scopus subject areas

  • Mathematics(all)


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