Craw, A. (2011) Quiver flag varieties and multigraded linear series. Duke Mathematical Journal, 156(3), pp. 469-500. (doi: 10.1215/00127094-2010-217)
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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<sub>θ</sub>(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<sub>X</sub>,E_1,...,E<sub>ρ</sub>)</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<sub>i</sub></b></i> is globally generated, we obtain a morphism <i><b>φ<sub>|<u>E</u>|</sub> : X -> |<u>E</u>|</b></i> realising each <i><b>E<sub>i</sub></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 |
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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 |
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Quiver flag varieties and multigraded linear series. (deposited 14 Sep 2010 15:02)
- Quiver flag varieties and multigraded linear series. (deposited 21 Feb 2011 13:48) [Currently Displayed]
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