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 languageEnglish
Pages (from-to)185–199
Number of pages15
JournalEuropean Journal of Mathematics
Volume4
Issue number1
Early online date7 Nov 2017
DOIs
Publication statusPublished - 1 Mar 2018

Fingerprint

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

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

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

Research output: Contribution to journalArticle

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