The D-equivalence conjecture for hyper-Kähler varieties via hyperholomorphic bundles
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910969276399616 |
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| author | Maulik, Davesh Shen, Junliang Yin, Qizheng Zhang, Ruxuan |
| author_facet | Maulik, Davesh Shen, Junliang Yin, Qizheng Zhang, Ruxuan |
| contents | We show that birational hyper-Kähler varieties of $K3^{[n]}$-type are derived equivalent, establishing the D-equivalence conjecture in these cases. The Fourier-Mukai kernels of our derived equivalences are constructed from projectively hyperholomorphic bundles, following ideas of Markman. Our method also proves a stronger version of the D-equivalence conjecture for hyper-Kähler varieties of $K3^{[n]}$-type with Brauer classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14775 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The D-equivalence conjecture for hyper-Kähler varieties via hyperholomorphic bundles Maulik, Davesh Shen, Junliang Yin, Qizheng Zhang, Ruxuan Algebraic Geometry We show that birational hyper-Kähler varieties of $K3^{[n]}$-type are derived equivalent, establishing the D-equivalence conjecture in these cases. The Fourier-Mukai kernels of our derived equivalences are constructed from projectively hyperholomorphic bundles, following ideas of Markman. Our method also proves a stronger version of the D-equivalence conjecture for hyper-Kähler varieties of $K3^{[n]}$-type with Brauer classes. |
| title | The D-equivalence conjecture for hyper-Kähler varieties via hyperholomorphic bundles |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2408.14775 |