Donaldson-Thomas theory for categories of homological dimension one with potential

Abstract

The aim of the paper is twofold. Firstly, we give an axiomatic presentation of Donaldson-Thomas theory for categories of homological dimension at most one with potential. In particular, we provide rigorous proofs of all standard results concerning the integration map, wall-crossing, PT-DT correspondence, etc. following Kontsevich and Soibelman. We also show the equivalence of their approach and the one given by Joyce and Song. Secondly, we relate Donaldson-Thomas functions for such a category with arbitrary potential to those with zero potential under some mild conditions. As a result of this, we obtain a geometric interpretation of Donaldson-Thomas functions in all known realizations, i.e. mixed Hodge modules, perverse sheaves and constructible functions.

80 pages

References in corpus (2)

• Donaldson-Thomas invariants vs. intersection cohomology for categories of homological dimension one
• An approach to F_1 via the theory of lambda rings

Cited by in corpus (11)

• The integrality conjecture and the cohomology of preprojective stacks
• Hall algebras in the derived category and higher rank DT invariants
• Cohomological Donaldson-Thomas theory of a quiver with potential and quantum enveloping algebras
• K-theoretic Hall algebras for quivers with potential
• Scattering diagrams of quivers with potentials and mutations
• Donaldson-Thomas invariants vs. intersection cohomology for categories of homological dimension one
• On the wall-crossing formula for quadratic differentials
• Positivity for quantum cluster algebras
• Deformed dimensional reduction
• An introduction into (motivic) Donaldson-Thomas theory
• Equivariant motivic Hall algebras