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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Bibliographic Information
- S. Feyzbakhsh
- Affiliation: Department of Mathematics, Imperial College, London SW7 2AZ, United Kingdom
- MR Author ID: 1394327
- Email: s.feyzbakhsh@imperial.ac.uk
- R. P. Thomas
- Affiliation: Department of Mathematics, Imperial College, London SW7 2AZ, United Kingdom
- MR Author ID: 636321
- ORCID: 0000-0002-7585-9691
- Email: richard.thomas@imperial.ac.uk
- Received by editor(s): October 19, 2021
- Received by editor(s) in revised form: March 5, 2022
- Published electronically: May 27, 2022
- Additional Notes: This work was supported by an EPSRC postdoctoral fellowship EP/T018658/1, an EPSRC grant EP/R013349/1 and a Royal Society research professorship
- © Copyright 2022 American Mathematical Society
- Journal: J. Amer. Math. Soc. 36 (2023), 795-826
- MSC (2020): Primary 14N35
- DOI: https://doi.org/10.1090/jams/1006
- MathSciNet review: 4583775