Full exceptional collections on Fano threefolds and groups generated by spherical twists on K3 surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910021257789440 |
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| author | Nordskova, Anya Bergh, Michel Van den |
| author_facet | Nordskova, Anya Bergh, Michel Van den |
| contents | For a Fano threefold admitting a full exceptional collection of vector bundles of length four we show that all full exceptional collections consist of shifted vector bundles. We prove this via a detailed study of the group generated by spherical twists on an anticanonical divisor. For example, we prove that this group is free and provide explicit generators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06023 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Full exceptional collections on Fano threefolds and groups generated by spherical twists on K3 surfaces Nordskova, Anya Bergh, Michel Van den Algebraic Geometry 14J45, 14J28, 18E30 For a Fano threefold admitting a full exceptional collection of vector bundles of length four we show that all full exceptional collections consist of shifted vector bundles. We prove this via a detailed study of the group generated by spherical twists on an anticanonical divisor. For example, we prove that this group is free and provide explicit generators. |
| title | Full exceptional collections on Fano threefolds and groups generated by spherical twists on K3 surfaces |
| topic | Algebraic Geometry 14J45, 14J28, 18E30 |
| url | https://arxiv.org/abs/2412.06023 |