Rank $r$ DT theory from rank $1$
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866917850467270656 |
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| author | Feyzbakhsh, Soheyla Thomas, Richard P. |
| author_facet | Feyzbakhsh, Soheyla Thomas, Richard P. |
| contents | 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 $X$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2108_02828 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Rank $r$ DT theory from rank $1$ Feyzbakhsh, Soheyla Thomas, Richard P. Algebraic Geometry High Energy Physics - Theory Symplectic Geometry 14N35 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 $X$. |
| title | Rank $r$ DT theory from rank $1$ |
| topic | Algebraic Geometry High Energy Physics - Theory Symplectic Geometry 14N35 |
| url | https://arxiv.org/abs/2108.02828 |