DonaldsonThomas invariants of length 2 flops
Abstract
We develop theoretical aspects of refined DonaldsonThomas theory for threefold flopping contractions, and use these to determine all DT invariants for infinite families of length 2 flops. Our results show that a refined version of the strongrationality conjecture of PandharipandeThomas holds in this setting, and also that refined DT invariants do not determine flops. Our main innovation is the application of tilting theory to better understand the stability conditions and cyclic $A_\infty$deformation theory of these spaces. Where possible we work in the motivic setting, but we also compute intermediary refinements, such as mixed Hodge structures.
 Publication:

arXiv eprints
 Pub Date:
 August 2020
 arXiv:
 arXiv:2008.02591
 Bibcode:
 2020arXiv200802591V
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Representation Theory;
 14N35 (Primary) 14E30 (Secondary)
 EPrint:
 48 pages