AI 中文总结
研究具有大皮卡数的超凯勒流形与阿贝尔簇的联系，核心方法是推广莫里森对（修正）小田猜想的解答，主要贡献是将该定理推广到K3曲面上的点希尔伯特概型等超凯勒流形例子。
AI 中文摘要
在本笔记中，我们探讨了具有大皮卡数的超凯勒流形与阿贝尔簇之间的联系。特别地，我们关注莫里森对（修正后的）小田猜想的解答：每个皮卡群足够大（在某种精确意义下）的K3曲面必定通过代数对应与一个阿贝尔曲面相关。我们将此定理推广到超凯勒流形的已知例子情形，如K3曲面上的点希尔伯特概型。
英文摘要
In this note, we explore the connection between hyperkähler manifolds with large Picard numbers and abelian varieties. In particular, we are interested in Morrison's solution to the (modified) Oda's conjecture: every K3 surface whose Picard group is large enough (in a certain precise sense) must be related via an algebraic correspondence to an abelian surface. We generalize this theorem to the case of known examples of hyperkähler manifolds such as pointed Hilbert schemes on K3 surfaces.
Comments8 pages, comments are welcome
