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.
Keywords
Cite
@article{arxiv.1512.08898,
title = {Donaldson-Thomas theory for categories of homological dimension one with potential},
author = {Ben Davison and Sven Meinhardt},
journal= {arXiv preprint arXiv:1512.08898},
year = {2015}
}
Comments
80 pages