Open Access
October 2018 Collapsing K3 surfaces and Moduli compactification
Yuji Odaka, Yoshiki Oshima
Proc. Japan Acad. Ser. A Math. Sci. 94(8): 81-86 (October 2018). DOI: 10.3792/pjaa.94.81


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.


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Yuji Odaka. Yoshiki Oshima. "Collapsing K3 surfaces and Moduli compactification." Proc. Japan Acad. Ser. A Math. Sci. 94 (8) 81 - 86, October 2018.


Published: October 2018
First available in Project Euclid: 29 September 2018

zbMATH: 07043484
MathSciNet: MR3859764
Digital Object Identifier: 10.3792/pjaa.94.81

Primary: 14J28
Secondary: 14H15 , 14J33 , 14T05 , 32M15 , 32Q25 , 53C26

Keywords: K3 surfaces , Kähler-Einstein metrics , locally symmetric spaces , moduli , Satake compactification , Tropical geometry

Rights: Copyright © 2018 The Japan Academy

Vol.94 • No. 8 • October 2018
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