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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2016
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1609.08340 |
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| _version_ | 1866917566523375616 |
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| author | Aprodu, Marian Costa, Laura Miro-Roig, Rosa Maria |
| author_facet | Aprodu, Marian Costa, Laura Miro-Roig, Rosa Maria |
| contents | In this short note, we study the existence problem for Ulrich bundles on ruled surfaces, focusing our attention on the smallest possible rank. We show that existence of Ulrich line bundles occurs if and only if the coefficient $α$ of the minimal section in the numerical class of the polarization equals one. For other polarizations, we prove the existence of rank two Ulrich bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1609_08340 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Ulrich bundles on ruled surfaces Aprodu, Marian Costa, Laura Miro-Roig, Rosa Maria Algebraic Geometry In this short note, we study the existence problem for Ulrich bundles on ruled surfaces, focusing our attention on the smallest possible rank. We show that existence of Ulrich line bundles occurs if and only if the coefficient $α$ of the minimal section in the numerical class of the polarization equals one. For other polarizations, we prove the existence of rank two Ulrich bundles. |
| title | Ulrich bundles on ruled surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/1609.08340 |