Quiver flag varieties and multigraded linear series

Craw, A. (2011) Quiver flag varieties and multigraded linear series. Duke Mathematical Journal, 156(3), pp. 469-500. (doi: 10.1215/00127094-2010-217)

This is the latest version of this item.

Full text not currently available from Enlighten.

Abstract

This paper introduces a class of smooth projective varieties that generalise and share many properties with partial flag varieties of type <i><b>A</b></i>. The quiver flag variety <i><b>M_θ(Q,<u>r</u></b></i>) of a finite acyclic quiver <b><i>Q</i></b> (with a unique source) and a dimension vector <i><b><u>r</u></b></i> is a fine moduli space of stable representations of <b><i>Q</i></b>. Quiver flag varieties are Mori Dream Spaces, they are obtained via a tower of Grassmann bundles, and their bounded derived category of coherent sheaves is generated by a tilting bundle. We define the multigraded linear series of a weakly exceptional sequence of locally free sheaves <b><i><u>E</u> = (O_X,E_1,...,E_ρ)</i></b> on a projective scheme <b>X</b> to be the quiver flag variety <b><i>|<u>E</u>|= Mθ(Q,<u>r</u>)</i></b> of a pair <b><i>(Q,<u>r</u></i></b>) encoded by <b><i><u>E</u></i></b>. When each <i><b>E_i</b></i> is globally generated, we obtain a morphism <i><b>φ_|<u>E</u>| : X -> |<u>E</u>|</b></i> realising each <i><b>E_i</b></i> as the pullback of a tautological bundle. As an application we introduce the multigraded Plucker embedding of a quiver flag variety

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Craw, Dr Alastair
• Authors: Craw, A.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics
• Journal Name: Duke Mathematical Journal
• Publisher: Duke University Press
• ISSN: 0012-7094
• ISSN (Online): 1547-7398

Related URLs

• Other

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
48001	1	Noncommutative toric geometry and multilinear series	Alastair Craw	Engineering & Physical Sciences Research Council (EPSRC)	EP/G004048/1	Mathematics