Ulrich bundles on cyclic coverings of projective spaces
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916794591084544 |
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| author | Parameswaran, A. J. Pine, Jagadish |
| author_facet | Parameswaran, A. J. Pine, Jagadish |
| contents | We prove the existence of Ulrich bundles on cyclic coverings of $\mathbb{P}^n$ of arbitrary degree $d$. Given a relatively Ulrich bundle on a complete intersection subvariety, we construct a relatively Ulrich bundle on the ambient variety. As an application, we prove that there exists a rank $d$ Ulrich bundle on generic cyclic coverings of $\mathbb{P}^2$ of degree $d$ such that the degree of the branch divisor $d \cdot k$ is even. When $d \cdot k$ is odd, we also provide an estimation of the rank of the Ulrich bundle on generic cyclic coverings of $\mathbb{P}^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10837 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ulrich bundles on cyclic coverings of projective spaces Parameswaran, A. J. Pine, Jagadish Algebraic Geometry 14H30 14H60 14J60 14M10 We prove the existence of Ulrich bundles on cyclic coverings of $\mathbb{P}^n$ of arbitrary degree $d$. Given a relatively Ulrich bundle on a complete intersection subvariety, we construct a relatively Ulrich bundle on the ambient variety. As an application, we prove that there exists a rank $d$ Ulrich bundle on generic cyclic coverings of $\mathbb{P}^2$ of degree $d$ such that the degree of the branch divisor $d \cdot k$ is even. When $d \cdot k$ is odd, we also provide an estimation of the rank of the Ulrich bundle on generic cyclic coverings of $\mathbb{P}^2$. |
| title | Ulrich bundles on cyclic coverings of projective spaces |
| topic | Algebraic Geometry 14H30 14H60 14J60 14M10 |
| url | https://arxiv.org/abs/2408.10837 |