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

• 成果类型: Article
• 署名作者: Maulik, Davesh; Shen, Junliang; Yin, Qizheng; Zhang, Ruxuan
• 署名单位: Massachusetts Institute of Technology (MIT); Yale University; Peking University; Fudan University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01339-8
• 发表日期: 2025
• 页码: 309-324
• 关键词: mori cones; kahler; flops

摘要

We show that birational hyper-K & auml;hler 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 & auml;hler varieties of K3[n]-type with Brauer classes.