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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2507.17681 |
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| _version_ | 1866915677454991360 |
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| author | Ito, Daigo Olander, Noah |
| author_facet | Ito, Daigo Olander, Noah |
| contents | We give a complete characterization of the line bundles on a proper variety whose tensor powers generate the derived category, answering a 2010 question of Chris Brav. The condition is analogous to the Nakai--Moishezon criterion and can be stated purely in terms of classical notions of positivity of line bundles. There is also a generalization which works for all Noetherian schemes. We use our criterion to prove basic properties of such line bundles and provide non-trivial examples of them. As an application, we give new examples of varieties which can be reconstructed from their derived categories in the sense of the Bondal--Orlov Reconstruction Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17681 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A derived category analogue of the Nakai--Moishezon criterion Ito, Daigo Olander, Noah Algebraic Geometry We give a complete characterization of the line bundles on a proper variety whose tensor powers generate the derived category, answering a 2010 question of Chris Brav. The condition is analogous to the Nakai--Moishezon criterion and can be stated purely in terms of classical notions of positivity of line bundles. There is also a generalization which works for all Noetherian schemes. We use our criterion to prove basic properties of such line bundles and provide non-trivial examples of them. As an application, we give new examples of varieties which can be reconstructed from their derived categories in the sense of the Bondal--Orlov Reconstruction Theorem. |
| title | A derived category analogue of the Nakai--Moishezon criterion |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2507.17681 |