Rank $r$ DT theory from rank $0$
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915037672636416 |
|---|---|
| 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 $r\ge1$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_02915 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Rank $r$ DT theory from rank $0$ Feyzbakhsh, Soheyla Thomas, Richard P. Algebraic Geometry High Energy Physics - Theory 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 $r\ge1$ 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. |
| title | Rank $r$ DT theory from rank $0$ |
| topic | Algebraic Geometry High Energy Physics - Theory 14N35 |
| url | https://arxiv.org/abs/2103.02915 |