On the Orlov conjecture for hyper-Kähler varieties via hyperholomorphic bundles
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915758729068544 |
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| author | Maulik, Davesh Shen, Junliang Yin, Qizheng |
| author_facet | Maulik, Davesh Shen, Junliang Yin, Qizheng |
| contents | We study Fourier transforms induced by Markman's projectively hyperholomorphic bundles on products of hyper-Kähler varieties of $K3^{[n]}$-type. As applications, we prove the following. (a) Derived equivalent hyper-Kähler varieties of $K3^{[n]}$-type have isomorphic homological motives preserving the cup-product. (b) All smooth projective moduli spaces of stable sheaves on a given $K3$ surface have isomorphic homological motives preserving the cup-product. (c) Assuming the Franchetta properties for the self-products of polarized $K3$ surfaces, the isomorphisms in (b) can be lifted to Chow motives for $K3$ surfaces of Picard rank 1. These results provide evidence for the Orlov conjecture and a conjecture of Fu-Vial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20289 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Orlov conjecture for hyper-Kähler varieties via hyperholomorphic bundles Maulik, Davesh Shen, Junliang Yin, Qizheng Algebraic Geometry We study Fourier transforms induced by Markman's projectively hyperholomorphic bundles on products of hyper-Kähler varieties of $K3^{[n]}$-type. As applications, we prove the following. (a) Derived equivalent hyper-Kähler varieties of $K3^{[n]}$-type have isomorphic homological motives preserving the cup-product. (b) All smooth projective moduli spaces of stable sheaves on a given $K3$ surface have isomorphic homological motives preserving the cup-product. (c) Assuming the Franchetta properties for the self-products of polarized $K3$ surfaces, the isomorphisms in (b) can be lifted to Chow motives for $K3$ surfaces of Picard rank 1. These results provide evidence for the Orlov conjecture and a conjecture of Fu-Vial. |
| title | On the Orlov conjecture for hyper-Kähler varieties via hyperholomorphic bundles |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2601.20289 |