A simple derived categorical generalization of Ulrich bundles
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908541834493952 |
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| author | Yoshida, Tomoki |
| author_facet | Yoshida, Tomoki |
| contents | We define special objects, Ulrich objects, on a derived category of polarized smooth projective variety as a generalization of Ulrich bundles to the derived category. These are defined by the cohomological conditions that are the same form as a cohomological criterion determining Ulrichness for sheaves. This paper gives a characterization of the Ulrich object similar to the one in [ES03]. As an application, we have provided a new approach to the Eisenbud-Schreyer question by using the notions of the generator of the derived category. We also have given an example of Ulrich objects that are not sheaf by Yoneda extensions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_05848 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A simple derived categorical generalization of Ulrich bundles Yoshida, Tomoki Algebraic Geometry 14F08 (primary), 14J60, 14D20 (secondary) We define special objects, Ulrich objects, on a derived category of polarized smooth projective variety as a generalization of Ulrich bundles to the derived category. These are defined by the cohomological conditions that are the same form as a cohomological criterion determining Ulrichness for sheaves. This paper gives a characterization of the Ulrich object similar to the one in [ES03]. As an application, we have provided a new approach to the Eisenbud-Schreyer question by using the notions of the generator of the derived category. We also have given an example of Ulrich objects that are not sheaf by Yoneda extensions. |
| title | A simple derived categorical generalization of Ulrich bundles |
| topic | Algebraic Geometry 14F08 (primary), 14J60, 14D20 (secondary) |
| url | https://arxiv.org/abs/2502.05848 |