A geometric compactification of moduli of K3 surfaces via tropical geometry

Date
2018/06/15 Fri 10:30 - 12:00
Room
3号館152号室
Speaker
Yuji Odaka
Affiliation
Kyoto university
Abstract

I will present an overview of my recent joint work with Yoshiki Oshima (cf., arXiv:1805.01724). We provide an explicit and global moduli-theoretic framework for collapsing limiting behavior of Ricci-flat Kahler metrics, and we use it to study especially the K3 surfaces case. In particular, explicit geometric compactifications of moduli of K3 surfaces or the abelian varieties, with parametrization of ``tropical geometric objects” at the boundary are provided. Our results also give a proof of a conjecture by Kontsevich-Soibelman (and Gross-Wilson) in the case of K3 surfaces as a byproduct.