Duke Mathematical Journal
- Duke Math. J.
- Volume 156, Number 3 (2011), 469-500.
Quiver flag varieties and multigraded linear series
This paper introduces a class of smooth projective varieties that generalize and share many properties with partial flag varieties of type . The quiver flag variety of a finite acyclic quiver (with a unique source) and a dimension vector is a fine moduli space of stable representations of . 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 on a projective scheme to be the quiver flag variety of a pair encoded by . When each is globally generated, we obtain a morphism , realizing each as the pullback of a tautological bundle. As an application, we introduce the multigraded Plücker embedding of a quiver flag variety.
Duke Math. J., Volume 156, Number 3 (2011), 469-500.
First available in Project Euclid: 9 February 2011
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14D22: Fine and coarse moduli spaces 16G20: Representations of quivers and partially ordered sets 18E30: Derived categories, triangulated categories
Secondary: 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 14M25: Toric varieties, Newton polyhedra [See also 52B20]
Craw, Alastair. Quiver flag varieties and multigraded linear series. Duke Math. J. 156 (2011), no. 3, 469--500. doi:10.1215/00127094-2010-217. https://projecteuclid.org/euclid.dmj/1297258907