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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2108.13314 |
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| _version_ | 1866910690421243904 |
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| author | Lee, Eunjeong Park, Kyeong-Dong |
| author_facet | Lee, Eunjeong Park, Kyeong-Dong |
| contents | We classify fourfolds with trivial canonical bundle which are zero loci of general global sections of completely reducible equivariant vector bundles over exceptional homogeneous varieties of Picard number one. By computing their Hodge numbers, we see that there exist no hyperkähler fourfolds among them. This implies that a hyperkähler fourfold represented as the zero locus of a general global section of a completely reducible equivariant vector bundle over a rational homogeneous variety of Picard number one is one of the two cases described by Beauville--Donagi and Debarre--Voisin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_13314 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Complete intersection hyperkähler fourfolds with respect to equivariant vector bundles over rational homogeneous varieties of Picard number one Lee, Eunjeong Park, Kyeong-Dong Algebraic Geometry Differential Geometry Representation Theory 14J35, 53C26 (Primary), 14M15, 14J60 (Secondary) We classify fourfolds with trivial canonical bundle which are zero loci of general global sections of completely reducible equivariant vector bundles over exceptional homogeneous varieties of Picard number one. By computing their Hodge numbers, we see that there exist no hyperkähler fourfolds among them. This implies that a hyperkähler fourfold represented as the zero locus of a general global section of a completely reducible equivariant vector bundle over a rational homogeneous variety of Picard number one is one of the two cases described by Beauville--Donagi and Debarre--Voisin. |
| title | Complete intersection hyperkähler fourfolds with respect to equivariant vector bundles over rational homogeneous varieties of Picard number one |
| topic | Algebraic Geometry Differential Geometry Representation Theory 14J35, 53C26 (Primary), 14M15, 14J60 (Secondary) |
| url | https://arxiv.org/abs/2108.13314 |