Birational geometry of Fano varieties of lines on cubic fourfolds containing pairs of cubic scrolls
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915484767617024 |
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| author | Brooke, Corey Frei, Sarah Marquand, Lisa Qin, Xuqiang |
| author_facet | Brooke, Corey Frei, Sarah Marquand, Lisa Qin, Xuqiang |
| contents | We characterize the birational geometry of some hyperkähler fourfolds of Picard rank $3$ obtained as the Fano varieties of lines on cubic fourfolds containing pairs of cubic scrolls. In each of the two cases considered, we identify all of the birational models, relating each model to familiar geometric constructions, and give explicit birational maps between them. We also provide structural results about the birational automorphism groups, giving generators in both cases and a full set of relations in one case. Finally, as a byproduct of our analysis, we obtain non-isomorphic cubic fourfolds whose Fano varieties of lines are birationally equivalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18904 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Birational geometry of Fano varieties of lines on cubic fourfolds containing pairs of cubic scrolls Brooke, Corey Frei, Sarah Marquand, Lisa Qin, Xuqiang Algebraic Geometry 14J42, 14E08, 14E07, 14J35 We characterize the birational geometry of some hyperkähler fourfolds of Picard rank $3$ obtained as the Fano varieties of lines on cubic fourfolds containing pairs of cubic scrolls. In each of the two cases considered, we identify all of the birational models, relating each model to familiar geometric constructions, and give explicit birational maps between them. We also provide structural results about the birational automorphism groups, giving generators in both cases and a full set of relations in one case. Finally, as a byproduct of our analysis, we obtain non-isomorphic cubic fourfolds whose Fano varieties of lines are birationally equivalent. |
| title | Birational geometry of Fano varieties of lines on cubic fourfolds containing pairs of cubic scrolls |
| topic | Algebraic Geometry 14J42, 14E08, 14E07, 14J35 |
| url | https://arxiv.org/abs/2407.18904 |