A geometric compactification of moduli of K3 surfaces via tropical geometry

開催日時
2018/06/15 金 10:30 - 12:00
場所
3号館152号室
講演者
尾高悠志
講演者所属
京都大学
概要

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.