Motivic DT/PT Correspondence

2025/11/27 by Chih-Huan Chang, Chang, Chih-Huan
Mathematics · #Geometry and complex manifolds #Advanced Combinatorial Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2511.22213

Abstract

We prove a motivic version of the Donaldson--Thomas/Pandharipande--Thomas (DT/PT) correspondence on Calabi--Yau threefolds. The proof combines Toda's wall crossing framework and the motivic integral identity recently proved by Bu. This provides a refinement of the numerical DT/PT correspondence.

Citations

• Orthosymplectic Donaldson-Thomas theory
• Intrinsic Donaldson-Thomas theory. II. Stability measures and invariants
• Cohomological Hall algebras for 3-Calabi-Yau categories
• A motivic integral identity for (-1)-shifted symplectic stacks
• Orientation data for moduli spaces of coherent sheaves over Calabi-Yau 3-folds
• The étale local structure of algebraic stacks
• Hall algebras in the derived category and higher rank DT invariants
• Donaldson-Thomas theory for categories of homological dimension one with potential
• Moduli of Bridgeland semistable objects on 3-folds and Donaldson-Thomas invariants
• On the structure of instability in moduli theory
• On motivic vanishing cycles of critical loci
• A 'Darboux theorem' for derived schemes with shifted symplectic structure
• Shifted Symplectic Structures
• Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex
• Hall algebras and curve-counting invariants
• An introduction to motivic Hall algebras
• Motivic Donaldson-Thomas invariants: summary of results
• Motivic degree zero Donaldson-Thomas invariants
• Curve counting theories via stable objects I. DT/PT correspondence
• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Good moduli spaces for Artin stacks
• Motivic invariants of Artin stacks and 'stack functions'
• Configurations in abelian categories. II. Ringel-Hall algebras
• Power structure over the Grothendieck ring of varieties and generating series of Hilbert schemes of points
• Gromov-Witten theory and Donaldson-Thomas theory, II
• Gromov-Witten theory and Donaldson-Thomas theory, I

Related

• Note on the motivic DT/PT correspondence and the motivic Flop formula
• Framed motivic Donaldson-Thomas invariants of small crepant resolutions
• A motivic integral identity for (-1)-shifted symplectic stacks
• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Motivic Donaldson--Thomas invariants of some quantized threefolds