Ulrich subvarieties and the non-existence of low rank Ulrich bundles on complete intersections
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913578391437312 |
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| author | Lopez, Angelo Felice Raychaudhury, Debaditya |
| author_facet | Lopez, Angelo Felice Raychaudhury, Debaditya |
| contents | We characterize the existence of an Ulrich vector bundle on a variety $X \subset P^N$ in terms of the existence of a subvariety satisfying some precise conditions. Then we use this fact to prove that a complete intersection of dimension $n \ge 4$, which if $n=4$ is very general and not of type $(2,2)$, does not carry any Ulrich bundles of rank $r \le 3$ unless $n=4, r=2$ and $X$ is a quadric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01154 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ulrich subvarieties and the non-existence of low rank Ulrich bundles on complete intersections Lopez, Angelo Felice Raychaudhury, Debaditya Algebraic Geometry We characterize the existence of an Ulrich vector bundle on a variety $X \subset P^N$ in terms of the existence of a subvariety satisfying some precise conditions. Then we use this fact to prove that a complete intersection of dimension $n \ge 4$, which if $n=4$ is very general and not of type $(2,2)$, does not carry any Ulrich bundles of rank $r \le 3$ unless $n=4, r=2$ and $X$ is a quadric. |
| title | Ulrich subvarieties and the non-existence of low rank Ulrich bundles on complete intersections |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2405.01154 |