Rank 𝑟 DT theory from rank 1

Feyzbakhsh, S.; Thomas, R.

doi:10.1090/jams/1006

Rank $r$ DT theory from rank $1$
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by S. Feyzbakhsh and R. P. Thomas

J. Amer. Math. Soc. 36 (2023), 795-826

DOI: https://doi.org/10.1090/jams/1006

Published electronically: May 27, 2022

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

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