Ulrich bundles on smooth toric threefolds with Picard number $2$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910047961874432 |
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| author | Bhattacharya, Debojyoti Malaspina, Francesco |
| author_facet | Bhattacharya, Debojyoti Malaspina, Francesco |
| contents | In this paper, we study Ulrich bundles on smooth toric threefolds with Picard number$~2$, namely $\mathbb P(\mathcal O_{\mathbb P^{2}}(a_0) \oplus \mathcal O_{\mathbb P^{2}}(a_1))$. We construct resolutions and monads for Ulrich bundles of arbitrary rank, and provide explicit examples together with a complete classification of those arising as pullbacks from $\mathbb{P}^2$. As a consequence, we also show that these varieties are Ulrich wild. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09664 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ulrich bundles on smooth toric threefolds with Picard number $2$ Bhattacharya, Debojyoti Malaspina, Francesco Algebraic Geometry Primary: 14J60, Secondary: 13C14, 14F05, 14M25 In this paper, we study Ulrich bundles on smooth toric threefolds with Picard number$~2$, namely $\mathbb P(\mathcal O_{\mathbb P^{2}}(a_0) \oplus \mathcal O_{\mathbb P^{2}}(a_1))$. We construct resolutions and monads for Ulrich bundles of arbitrary rank, and provide explicit examples together with a complete classification of those arising as pullbacks from $\mathbb{P}^2$. As a consequence, we also show that these varieties are Ulrich wild. |
| title | Ulrich bundles on smooth toric threefolds with Picard number $2$ |
| topic | Algebraic Geometry Primary: 14J60, Secondary: 13C14, 14F05, 14M25 |
| url | https://arxiv.org/abs/2603.09664 |