Speaker: Prof. Zhiyuan Li (Shanghai Center for Mathematical Sciences)

Time: 10:35-11:35, Sep 25, 2020 (Beijing Time)

Abstract: The moduli spaces of quasi-polarized K3 surfaces of degree 2d are locally symmetric varieties. Consequently, they have natural projective compactifications from arithmetic, the Satake-Baily-Borel compactification. For low degree K3 surfaces, Mukai has shown that alternative projective models of their moduli spaces can be obtained by means of GIT. It is a natural question to compare Mukai's GIT models with Baily-Borel models. The case of degree 2 and 4 K3 surfaces were analyzed in detail by Shah, Looijenga, and more recently Laza and O' Grady. Their idea is the GIT models are coming a series of arithmetic birational modifications, i.e. the center of birational maps are Shimura subvarieties. In degree 4, this is so called Hassett-Keel-Looijenga (HKL) program. In thi talk, I will discuss the HKL program on K3 surfaces with Mukai models. This is a joint work with Greer, Laza, Tian and Si.