Compactifications of moduli space of K3 surfaces of degree 6

Compactifications of moduli space of K3 surfaces of degree 6

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Zhiyuan Li, Fudan University

Zoom link:  https://princeton.zoom.us/j/91248028438

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 talk about the HKL program on K3 surfaces with Mukai models. I will focus on the case of K3 surfaces of degree 6. I will also discuss the problem on the effective cone of SBB compactification.

This is an ongoing work with Greer, Laza, Tian and Si.