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

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arxiv 1512.08898 v1 pith:KYSHTT64 submitted 2015-12-30 math.AG math.CTmath.RT

Ben Davison , Sven Meinhardt This is my paper · ORCID
classification math.AGmath.CTmath.RT
keywords donaldson-thomaspotentialfunctionscategoriesdimensionhomologicaltheoryapproach
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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.

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Cited by 2 Pith papers

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  1. Cohomology of symmetric stacks

    math.AG 2025-02 conditional novelty 8.0 of 10

    A decomposition theorem for cohomology of symmetric stacks yields BPS cohomology, proving cohomological integrality for wide classes of moduli stacks and 3-Calabi-Yau categories.

  2. Wall-crossing formulas via spectral networks

    math.AG 2025-08 conditional novelty 7.0 of 10

    A self-contained geometric proof of the wall-crossing formula via path-lifting rules for spectral networks, including spiral domains, with the charge lattice generated by A0-laminations.

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