Rank $r$ DT theory from rank $0$

Abstract

Fix a Calabi-Yau 3-fold $X$ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda, such as the quintic 3-fold. We express Joyce's generalised DT invariants counting Gieseker semistable sheaves of any rank $r\ge 1$ on $X$ in terms of those counting sheaves of rank 0 and pure dimension 2. The basic technique is to reduce the ranks of sheaves by replacing them by the cokernels of their Mochizuki/Joyce-Song pairs and then use wall crossing to handle their stability.

arXiv commentAccepted version, referees' corrections. 44 pages, 6 figures

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Cited by in corpus (2)

• Curve counting and S-duality
• Scaling Black Holes and Modularity