English

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 XX 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 rr on XX in terms of those counting sheaves of rank 1. By the MNOP conjecture they are therefore determined by the Gromov-Witten invariants of XX.

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