The D-equivalence conjecture for hyper-Kähler varieties via hyperholomorphic bundles

Author(s)
Maulik, Davesh; Shen, Junliang; Yin, Qizheng; Zhang, Ruxuan
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Abstract
We show that birational hyper-Kähler varieties of K 3 [ 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 K 3 [ n ] -type with Brauer classes.
Date issued
2025-06-09
URI
https://hdl.handle.net/1721.1/159543
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Inventiones mathematicae
Publisher
Springer Berlin Heidelberg
Citation
Maulik, D., Shen, J., Yin, Q. et al. The D-equivalence conjecture for hyper-Kähler varieties via hyperholomorphic bundles. Invent. math. 241, 309–324 (2025).
Version: Author's final manuscript
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