Hall algebras and curve-counting invariants
Algebraic Geometry
2020-06-26 v3
Abstract
We use Joyce's theory of motivic Hall algebras to prove that reduced Donaldson-Thomas curve-counting invariants on Calabi-Yau threefolds coincide with stable pair invariants, and that the generating functions for these invariants are Laurent expansions of rational functions.
Cite
@article{arxiv.1002.4374,
title = {Hall algebras and curve-counting invariants},
author = {Tom Bridgeland},
journal= {arXiv preprint arXiv:1002.4374},
year = {2020}
}
Comments
38 pages. Version 2 corrected an error in the published paper kindly pointed out by Yukinobu Toda. Version 3 corrects a further error pointed out by Toda and Tasuki Kinjo. The only changes are footnotes on pages 27 and 38, together with new Sections 7.3 and 7.4 which explain the mistakes and how to fix them