Donaldson-Thomas invariants of length 2 flops
Abstract
We develop theoretical aspects of refined Donaldson-Thomas theory for threefold flops, and use these to determine all DT invariants for a doubly infinite family of length 2 flopping contractions. Our results show that a refined version of the strong-rationality conjecture of Pandharipande-Thomas holds in this setting, and also that refined DT invariants do not classify flops. Our main innovation is the application of tilting theory to better understand the stability conditions and cyclic A-infinity-deformation theory of these spaces. Where possible we work in the motivic setting, but we also compute intermediary refinements, such as mixed Hodge structures.
Cite
@article{arxiv.2008.02591,
title = {Donaldson-Thomas invariants of length 2 flops},
author = {Okke van Garderen},
journal= {arXiv preprint arXiv:2008.02591},
year = {2022}
}
Comments
56 pages, exposition and statement of theorems improved in several places, fixed an error in the proof of Prop 4.7