Quiver Flag Varieties and Multigraded Linear Series
نویسنده
چکیده
This paper introduces a class of smooth projective varieties that generalise and share many properties with partial flag varieties of type A. The quiver flag variety Mθ(Q, r) of a finite acyclic quiver Q (with a unique source) and a dimension vector r is a fine moduli space of stable representations of Q. 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 E = (OX , E1, . . . , Eρ) on a projective scheme X to be the quiver flag variety |E | := Mθ(Q, r) of a pair (Q, r) encoded by E . When each Ei is globally generated, we obtain a morphism φ|E | : X → |E | realising each Ei as the pullback of a tautological bundle. As an application we introduce the multigraded Plücker embedding of a quiver flag variety
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