WEEKLY ACTIVITIES

Time: 12h00, Friday, May 14, 2021

Session Chairs: Prof. JongHae Keum (KIAS)

Join Zoom Meeting: ZOOM ID：466 356 2952

Password：mcm1234

https://zoom.com.cn/j/4663562952?pwd=MytDVU9tUlg5LzFHNHRHZmFMZ0JaUT09

Abstract: What we mean by “geometric compactifications” in the title is it still parametrizes “geometric objects” at the boundary. In algebraic geometry, it is natural to expect degenerate varieties as such objects. For the moduli of polarized K3 surfaces (or K-trivial varieties in general) case, it is natural to expect slc and K-trivial degenerations, but there are many such compactifications for a fixed moduli component, showing flexibility / ambiguity / difficulty of the problem.This talk is planned to mainly focus the following.

In K3 surfaces (and hyperKahler varieties), there is a canonical geometric compactification whose boundary and parametrized objects are Not varieties but tropical geometric or with more PL flavor. This is ongoing joint work with Y.Oshima (cf., arXiv:1810.07685, 2010.00416).

aIn general, there is a canonical PARTIAL compactification (quasi-projective variety) of moduli of polarized K-trivial varieties (essentially due to Birkar and Zhang), as a completion with respect to the Weil-Petersson metric. This is characterized by K-stability.

For general information of the AGEA seminar, please check out

https://sites.google.com/ncts.ntu.edu.tw/agea-seminar

or the mirror site

http://www.math.ntu.edu.tw/~jkchen/agea-seminar.html

or the webpage on MCM

http://www.mcm.ac.cn/events/seminars/202102/t20210205_625406.html