Rank Two Sheaves With Low Discriminant on the Fano Threefold of Index 2 and Degree 5
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908810818355200 |
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| author | Vassiliev, Danil A. |
| author_facet | Vassiliev, Danil A. |
| contents | We describe rank 2 Gieseker semistable sheaves $E$ on the Fano threefold $X_5$ of index 2 and degree 5 with maximal third Chern class $c_3(E)$ for all possible low values of discriminant $\overlineΔ_H(E)\le 40$. The work uses the theory of tilt-stability and Bridgeland stability conditions on smooth projective threefolds. We also make a conjecture about the rank 2 sheaves on $X_5$ with maximal $c_3$ and discriminant big enough. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_10608 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rank Two Sheaves With Low Discriminant on the Fano Threefold of Index 2 and Degree 5 Vassiliev, Danil A. Algebraic Geometry 14J30 (Primary) 14D20, 14J60, 14F08 (Secondary) We describe rank 2 Gieseker semistable sheaves $E$ on the Fano threefold $X_5$ of index 2 and degree 5 with maximal third Chern class $c_3(E)$ for all possible low values of discriminant $\overlineΔ_H(E)\le 40$. The work uses the theory of tilt-stability and Bridgeland stability conditions on smooth projective threefolds. We also make a conjecture about the rank 2 sheaves on $X_5$ with maximal $c_3$ and discriminant big enough. |
| title | Rank Two Sheaves With Low Discriminant on the Fano Threefold of Index 2 and Degree 5 |
| topic | Algebraic Geometry 14J30 (Primary) 14D20, 14J60, 14F08 (Secondary) |
| url | https://arxiv.org/abs/2510.10608 |