Mori Dream Spaces as fine moduli of quiver representations

Craw, A. and Winn, D. (2013) Mori Dream Spaces as fine moduli of quiver representations. Journal of Pure and Applied Algebra, 217(1), pp. 172-189. (doi: 10.1016/j.jpaa.2012.06.014)

Abstract

We construct Mori Dream Spaces as fine moduli spaces of representations of bound quivers, thereby extending results of Craw–Smith [6] beyond the toric case. Any collection of effective line bundles 풪 ℒ=(풪X,L1,…,Lr) on a Mori Dream Space X defines a bound quiver of sections and a map from X to a toric quiver variety |ℒ| called the multigraded linear series. We provide necessary and sufficient conditions for this map to be a closed immersion and, under additional assumptions on ℒ, the image realises X as the fine moduli space of ϑ-stable representations of the bound quiver. As an application, we show how to reconstruct del Pezzo surfaces from a full, strongly exceptional collection of line bundles.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Craw, Dr Alastair and Winn, Ms Dorothy
• Authors: Craw, A., and Winn, D.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Pure and Applied Algebra
• Publisher: Elsevier
• ISSN: 0022-4049
• ISSN (Online): 1873-1376
• Published Online: 25 June 2012
• Copyright Holders: Copyright © 2002 Elsevier B.V.
• First Published: First published in Journal of Pure and Applied Alegbra 217(1): 172-189
• Publisher Policy: Reproduced in accordance with the publisher copyright policy

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