On quivers and tilting bundles on projective toric manifolds -- Alastair Craw

Abstract: I will describe how certain collections of line bundles on a projective toric manifold X can be used to construct X as a fine moduli space of quiver representations. If the line bundles form a full strong exceptional collection, then the tautological bundle arising form the moduli construction gives a presentation of the derived category of X. This programme leads to new examples of such collections, and hence to new examples where the derived category of a toric manifold is well understood. This is joint work with Gregory G. Smith.