Positivity of Ulrich bundles in the ample and free case
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929264980393984 |
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| author | Buttinelli, Valerio |
| author_facet | Buttinelli, Valerio |
| contents | We study the positivity of an Ulrich vector bundle defined with respect to a globally generated ample line bundle. First we prove a generalization of a Lopez theorem on the first Chern class and the bigness of an Ulrich bundle. Then, under some additional assumptions on the polarization, we give a description of its augmented base locus, which consequently leads to a characterization of the V-bigness and of the ampleness of an Ulrich bundle in this setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03139 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Positivity of Ulrich bundles in the ample and free case Buttinelli, Valerio Algebraic Geometry We study the positivity of an Ulrich vector bundle defined with respect to a globally generated ample line bundle. First we prove a generalization of a Lopez theorem on the first Chern class and the bigness of an Ulrich bundle. Then, under some additional assumptions on the polarization, we give a description of its augmented base locus, which consequently leads to a characterization of the V-bigness and of the ampleness of an Ulrich bundle in this setting. |
| title | Positivity of Ulrich bundles in the ample and free case |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2403.03139 |