Derived categories of small toric Calabi-Yau 3-folds and counting invariants

2008/09/17 by Kentaro Nagao, Nagao, Kentaro · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.0809.2994

openalex publication_date 2008/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We first construct a derived equivalence between a small crepant resolution of an affine toric Calabi-Yau 3-fold and a certain quiver with a superpotential. Under this derived equivalence we establish a wall-crossing formula for the generating function of the counting invariants of perverse coherent systems. As an application we provide certain equations on Donaldson-Thomas, Pandeharipande-Thomas and Szendroi's invariants. Finally, we show that moduli spaces associated with a quiver given by successive mutations are realized as the moduli spaces associated the original quiver by changing the stability conditions.

Citations

• On moduli spaces of quiver representations associated with dimer models
• Quiver varieties and Hilbert schemes
• Donaldson-Thomas invariants via microlocal geometry
• Graded Calabi Yau algebras of dimension 3
• Birational Calabi-Yau 3-folds and BPS state counting
• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Decomposition of Marsden–Weinstein Reductions for Representations of Quivers
• Refined open non-commutative Donaldson-Thomas invariants for small crepant resolutions

Cited by

• Crepant Resolutions, Quivers and GW/NCDT Duality

Related

• Counting invariant of perverse coherent sheaves and its wall-crossing
• Invariant Stability Conditions on Certain Calabi-Yau Threefolds
• Donaldson-Thomas theory for Calabi-Yau 4-folds
• Derived equivalences from mutations of quivers with potential
• Curve counting invariants around the conifold point