## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Collapsing K3 surfaces and Moduli compactification

#### Abstract

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.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 94, Number 8 (2018), 81-86.

Dates
First available in Project Euclid: 29 September 2018

https://projecteuclid.org/euclid.pja/1538186761

Digital Object Identifier
doi:10.3792/pjaa.94.81

Mathematical Reviews number (MathSciNet)
MR3859764

#### Citation

Odaka, Yuji; Oshima, Yoshiki. Collapsing K3 surfaces and Moduli compactification. Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 8, 81--86. doi:10.3792/pjaa.94.81. https://projecteuclid.org/euclid.pja/1538186761

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