报告题目：K-Moduli space of del pezzo pairs and K3 moduli spaces

报告人：司飞博士 北京大学

报告时间：2024年5月14日（星期二），上午10:00

报告地点：兴庆校区数学楼2-2会议室

报告摘要：A K3 surfaces together with an anti-symplectic involution can be identified with a pair (X , C) consisting of a del pezzo surface X with a curve C in the linear system |-2K_X|. In this talk, we will present a series of modular compactifications for their moduli space using K-stability. More precisely, we will give an explicit description of K-moduli space P^K(c) parametrizing K-polystable pairs (X, cC) when varying rational number c under the framework of wall-crossing for K-moduli space due to Ascher-DeVleming-Liu. Moreover, we will show that the K-moduli space P^K(c) is isomorphic to certain log canonical model on Baily-Borel compactification of the moduli space of K3 surfaces with anti-symplectic involution. This can be viewed as another example of Hassett-Keel-Looijenga program proposed by Laza-O’Grady. This is based on joint work with Long Pan and Haoyu Wu.

个人简介：司飞，现为北京大学国际数学研究中心博士后，2021年在复旦大学上海数学中取得博士学位，导师为陈猛教授和李志远教授。研究方向为代数几何，尤其是对代数几何中的模空间相关问题感兴趣。目前研究集中在如下领域：

（1）K3曲面模空间的同调理论和相交理论研究；

（2）研究利用几何不变量理论，霍奇理论以及代数K-稳定性理论来探索K3曲面的模空间的双有理几何，以及K-稳定性模空间的显示构造；

（3）模空间同调群的稳定现象，尤其是在曲面上稳定层的模空间上。