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arXiv · 2408.14775

The D-equivalence conjecture for hyper-K\"ahler varieties via hyperholomorphic bundles

Davesh Maulik·Junliang Shen·Qizheng Yin·Ruxuan Zhang
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Abstract

We show that birational hyper-K\"ahler 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-K\"ahler varieties of $K3^{[n]}$-type with Brauer classes.

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Davesh Maulik, Junliang Shen, Qizheng Yin, Ruxuan Zhang. 2024-08-27. The D-equivalence conjecture for hyper-K\"ahler varieties via hyperholomorphic bundles. https://arxiv.org/abs/2408.14775

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