Proceedings of the Japan Academy, Series A, Mathematical Sciences

Collapsing K3 surfaces and Moduli compactification

Yuji Odaka and Yoshiki Oshima

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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

Permanent link to this document
https://projecteuclid.org/euclid.pja/1538186761

Digital Object Identifier
doi:10.3792/pjaa.94.81

Mathematical Reviews number (MathSciNet)
MR3859764

Subjects
Primary: 14J28: $K3$ surfaces and Enriques surfaces
Secondary: 14J33: Mirror symmetry [See also 11G42, 53D37] 14T05: Tropical geometry [See also 12K10, 14M25, 14N10, 52B20] 14H15: Families, moduli (analytic) [See also 30F10, 32G15] 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15] 53C26: Hyper-Kähler and quaternionic Kähler geometry, "special" geometry 32Q25: Calabi-Yau theory [See also 14J30]

Keywords
Locally symmetric spaces Satake compactification Kähler-Einstein metrics K3 surfaces Moduli tropical geometry

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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