数学科学学院学术报告[2024] 134号

(高水平大学建设系列报告1014号)

报告题目: Kuga-Satake construction on families of K3 surfaces of Picard rank 14

报告人：Flora Wing Kei Poon

报告时间：2024年12月17日14:00-15:00

讲座地点：汇文楼1420

报告内容：Classically, it is known that the period domain D of a moduli space of K3 surfaces of Picard rank r > 13 is isometric to the period domain of a different moduli space of some polarized varieties. The lowest Picard rank known for such a coincidence happens is r = 14: there is an isometry from D to the period domain of a moduli of polarized abelian 8-folds with totally definite quaternion multiplication, which descends to a diffeomorphism between the corresponding moduli spaces. We will describe the latter map explicitly by considering the Kuga-Satake construction on lattice polarized K3 surfaces. Using lattice theoretical arguments, one can also show that the map of moduli exhibits exceptional behaviour when specialised to families of K3 surfaces of Picard rank 18 admitting a Shioda-Inose or a Kummer structure.

报告人简介：Dr. Poon，现于National Center for Theoretical Sciences从事博士后研究。研究方向为Moduli of abelian varieties and K3 surfaces, locally symmetric varieties, Lie theory.

邀请人： 黄国坚

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