Hall algebras in the derived category and higher rank DT invariants

Abstract

We remark that the combination of the works of Ben-Bassat-Brav-Bussi-Joyce and Alper-Hall-Rydh imply the conjectured local description of the moduli stacks of semi-Schur objects in the derived category of coherent sheaves on projective Calabi-Yau 3-folds. This result was assumed in the author's previous papers to apply wall-crossing formulas of DT type invariants in the derived category, e.g. DT/PT correspondence, rationality, etc. We also show that the above result is applied to prove the higher rank version of DT/PT correspondence and rationality.

27 pages

References in corpus (7)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Donaldson-Thomas invariants via microlocal geometry
• Zero dimensional Donaldson-Thomas invariants of threefolds
• Donaldson-Thomas theory for categories of homological dimension one with potential
• On higher rank Donaldson-Thomas invariants
• Generalized Donaldson-Thomas theory over fields K $\ne$ C
• On motivic Joyce-Song formula for the Behrend function identities

Cited by in corpus (11)

• Curve counting on elliptic Calabi-Yau threefolds via derived categories
• Virtual counts on Quot schemes and the higher rank local DT/PT correspondence
• Donaldson-Thomas invariants of abelian threefolds and Bridgeland stability conditions
• Rank 2 wall-crossing and the Serre correspondence
• Weight functions, tilts, and stability conditions
• Hall algebras and Donaldson-Thomas invariants
• A relation between higher-rank PT stable objects and quotients of coherent sheaves
• Intrinsic Stabilizer Reduction and Generalized Donaldson-Thomas Invariants
• Note on the motivic DT/PT correspondence and the motivic Flop formula
• Fourier-Mukai transforms of slope stable torsion-free sheaves on Weierstrass elliptic surfaces
• Gromov--Witten/Pandharipande--Thomas correspondence via conifold transitions