Collapsing K3 surfaces and Moduli compactification

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Yuji Odaka¹  Yoshiki Oshima² 

[1] Department of Mathematics, Kyoto University;Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University

关键词: Locally symmetric spaces;    Satake compactification;    Ka¨hler-Einstein metrics;    K3 surfaces;    Moduli;    tropical geometry.;   

DOI  :  10.3792/pjaa.94.81

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

This note is a summary of our work [OO], which provides an explicit and global moduli-theoretic framework for the collapsing of Ricci-flat Kähler metrics and we use it to study especially the K3 surfaces case. For instance, it allows us to discuss their Gromov-Hausdorff limits along any sequences, which are even not necessarily “maximally degenerating”. Our results also give a proof of Kontsevich-Soibelman [KS06,Conjecture 1] (cf., [GW00, Conjecture 6.2]) in the case of K3 surfaces as a byproduct.

【 授权许可】

Unknown