Instanton Sheaves on Ruled Fano 3-folds of Picard Rank 2 and Index 1
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915780672618496 |
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| author | Genc, Ozhan Jardim, Marcos |
| author_facet | Genc, Ozhan Jardim, Marcos |
| contents | We study rank 2 $h$-instanton sheaves on projective threefolds. We demonstrate that any orientable rank 2, non-locally free $h$-instanton sheaf with defect 0 on a threefold can be obtained as an elementary transformation of a locally free $h$-instanton sheaf. Our focus then shifts to ruled Fano threefolds of Picard rank 2 and index 1, of which there are five deformation classes. We establish the existence of orientable rank 2 $h$-instanton bundles on such varieties. Additionally, we prove the existence of Ulrich bundles on such varieties, which correspond to $h$-instanton sheaves of minimum charge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22005 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Instanton Sheaves on Ruled Fano 3-folds of Picard Rank 2 and Index 1 Genc, Ozhan Jardim, Marcos Algebraic Geometry We study rank 2 $h$-instanton sheaves on projective threefolds. We demonstrate that any orientable rank 2, non-locally free $h$-instanton sheaf with defect 0 on a threefold can be obtained as an elementary transformation of a locally free $h$-instanton sheaf. Our focus then shifts to ruled Fano threefolds of Picard rank 2 and index 1, of which there are five deformation classes. We establish the existence of orientable rank 2 $h$-instanton bundles on such varieties. Additionally, we prove the existence of Ulrich bundles on such varieties, which correspond to $h$-instanton sheaves of minimum charge. |
| title | Instanton Sheaves on Ruled Fano 3-folds of Picard Rank 2 and Index 1 |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2410.22005 |