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arXiv · 1512.08898

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

Ben Davison·Sven Meinhardt
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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.

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Ben Davison, Sven Meinhardt. 2015-12-30. Donaldson-Thomas theory for categories of homological dimension one with potential. https://arxiv.org/abs/1512.08898

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