Rank $r$ DT theory from rank $1$
Algebraic Geometry
2024-12-02 v2 High Energy Physics - Theory
Symplectic Geometry
Abstract
Fix a Calabi-Yau 3-fold satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr\`i-Toda, such as the quintic 3-fold. We express Joyce's generalised DT invariants counting Gieseker semistable sheaves of any rank on in terms of those counting sheaves of rank 1. By the MNOP conjecture they are therefore determined by the Gromov-Witten invariants of .
Keywords
Cite
@article{arxiv.2108.02828,
title = {Rank $r$ DT theory from rank $1$},
author = {Soheyla Feyzbakhsh and Richard P. Thomas},
journal= {arXiv preprint arXiv:2108.02828},
year = {2024}
}
Comments
Referee's corrections, added one figure. To appear in JAMS. 33 pages, 4 figures