Moduli Spaces and Related Topics | Curves on K3 surfaces and Mukai’s program

Time：Wed., 14:00-15:00, Mar. 20. 2024

Venue：C654, Shuangqing Complex Building A 清华大学双清综合楼A座 C654

Organizer：Xiang He, Chenglong Yu, Dingxin Zhang, Jie Zhou

Speaker：Haoyu Wu (Fudan University)

Abstract:

The Mukai’s program seeks to recover a K3 surface X from any curve C on it by exhibiting it as a Fourier-Mukai partner to a Brill--Noether locus of vector bundles on the curve. In this talk, I will give an introduction to work of Feyzbakhsh for Picard number one K3 and primitive curve C. We extend the results to the case of non-primitive curves by introducing the tools of destabilizing regions. As an application, we show that there are hyper-K\"{a}hler varieties as Brill-Noether loci of curves in every dimension. This is a joint work with Yiran Chen and Zhiyuan Li.

DATEMarch 20, 2024

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