Crepant resolutions and brane tilings II: Tilting bundles

Abstract

Given a brane tiling, that is, a bipartite graph on a torus, we can associate with it a singular 3-Calabi-Yau variety. Using the brane tiling, we can also construct all crepant resolutions of the above variety. We give an explicit toric description of tilting bundles on these crepant resolutions. This result proves the conjecture of Hanany, Herzog and Vegh and a version of the conjecture of Aspinwall.

15 pages

References in corpus (7)

• Consistency conditions for brane tilings
• Dimer models and the special McKay correspondence
• On moduli spaces of quiver representations associated with dimer models
• Dimer models and Calabi-Yau algebras
• On the noncommutative Donaldson-Thomas invariants arising from brane tilings
• Crepant resolutions and brane tilings I: Toric realization
• D-Branes on Toric Calabi-Yau Varieties

Cited by in corpus (8)

• Dimer models and exceptional collections
• Geometric engineering of (framed) BPS states
• Remarks on quiver gauge theories from open topological string theory
• Combinatorial Reid's recipe for consistent dimer models
• HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants
• Exact Lefschetz fibrations associated with dimer models
• Attractor invariants, brane tilings and crystals
• Noncommutative mirror symmetry for punctured surfaces