Non-existence of low rank Ulrich bundles on Veronese varieties
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911914372628480 |
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| author | Lopez, Angelo Felice Raychaudhury, Debaditya |
| author_facet | Lopez, Angelo Felice Raychaudhury, Debaditya |
| contents | We show that Veronese varieties of dimension $n \ge 4$ do not carry any Ulrich bundles of rank $r \le 3$. In order to prove this, we prove that a Veronese embedding of a complete intersection of dimension $m \ge 4$, which if $m=4$ is either $\mathbb P^4$ or has degree $d \ge 2$ and is very general and not of type $(2), (2,2)$, does not carry any Ulrich bundles of rank $r \le 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08162 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-existence of low rank Ulrich bundles on Veronese varieties Lopez, Angelo Felice Raychaudhury, Debaditya Algebraic Geometry We show that Veronese varieties of dimension $n \ge 4$ do not carry any Ulrich bundles of rank $r \le 3$. In order to prove this, we prove that a Veronese embedding of a complete intersection of dimension $m \ge 4$, which if $m=4$ is either $\mathbb P^4$ or has degree $d \ge 2$ and is very general and not of type $(2), (2,2)$, does not carry any Ulrich bundles of rank $r \le 3$. |
| title | Non-existence of low rank Ulrich bundles on Veronese varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2406.08162 |