Moduli spaces for Bondal quivers

Abstract

Given a sufficiently nice collection of sheaves on an algebraic variety V, Bondal explained how to build a quiver Q along with an ideal of relations in the path algebra of Q such that the derived category of representations of Q subject to these relations is equivalent to the derived category of coherent sheaves on V. We consider the case in which these sheaves are all locally free and study the moduli spaces of semistable representations of our quiver with relations for various stability conditions. We show that V can often be recovered as a connected component of such a moduli space and we describe the line bundle induced by a GIT construction of the moduli space in terms of the input data. In certain special cases, we interpret our results in the language of topological string theory.

17 pages, major revision

References in corpus (3)

• Exceptional collections for Grassmannians of isotropic lines
• Projective toric varieties as fine moduli spaces of quiver representations
• Moduli Spaces for D-branes at the Tip of a Cone

Cited by in corpus (13)

• Exceptional Sequences of Invertible Sheaves on Rational Surfaces
• Quiver representations in toric geometry
• Moduli Spaces for D-branes at the Tip of a Cone
• Stability Conditions and Branes at Singularities
• Probing Geometry with Stability Conditions
• D-branes Wrapped on Fuzzy del Pezzo Surfaces
• A Note on Support in Triangulated Categories
• The McKay correspondence, tilting equivalences, and rationality
• Moduli of quiver representations for exceptional collections on surfaces
• Quiver GIT for Varieties with Tilting Bundles
• Blow ups of ${\mathbb{P}}^n$ as quiver moduli for exceptional collections
• Mori Dream Spaces as fine moduli of quiver representations
• Reconstructing the Grassmannian of lines from Kapranov's tilting bundle