Stronger Bogomolov--Gieseker type inequality on quintic threefold
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915706268811264 |
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| author | Xu, Chunkai |
| author_facet | Xu, Chunkai |
| contents | We establish a stronger Bogomolov--Gieseker type inequality for slope-semistable sheaves on the smooth quintic threefold. Our approach combines a refined restriction theorem for tilt-stable objects with explicit Clifford-type bounds for semistable bundles on plane quintic curves. As a consequence, we obtain an explicit piecewise linear inequality on the Chern characters of any slope-semistable sheaf improving upon the classical Bogomolov--Gieseker bound and implying Toda's conjectural inequality.
The method also yields a stronger Bogomolov--Gieseker type inequality on smooth quintic surfaces.
These results provide new evidence toward the existence of a Bridgeland stability condition of Gepner type on the quintic threefold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stronger Bogomolov--Gieseker type inequality on quintic threefold Xu, Chunkai Algebraic Geometry 14F06, 14F08 We establish a stronger Bogomolov--Gieseker type inequality for slope-semistable sheaves on the smooth quintic threefold. Our approach combines a refined restriction theorem for tilt-stable objects with explicit Clifford-type bounds for semistable bundles on plane quintic curves. As a consequence, we obtain an explicit piecewise linear inequality on the Chern characters of any slope-semistable sheaf improving upon the classical Bogomolov--Gieseker bound and implying Toda's conjectural inequality. The method also yields a stronger Bogomolov--Gieseker type inequality on smooth quintic surfaces. These results provide new evidence toward the existence of a Bridgeland stability condition of Gepner type on the quintic threefold. |
| title | Stronger Bogomolov--Gieseker type inequality on quintic threefold |
| topic | Algebraic Geometry 14F06, 14F08 |
| url | https://arxiv.org/abs/2511.21288 |