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arXiv · 2103.02915

Rank $r$ DT theory from rank $0$

Soheyla Feyzbakhsh·Richard P. Thomas
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Abstract

Fix a Calabi-Yau 3-fold $X$ 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 $r\ge1$ 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.

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Soheyla Feyzbakhsh, Richard P. Thomas. 2021-03-04. Rank $r$ DT theory from rank $0$. https://doi.org/10.1215/00127094-2023-0050

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