Proceedings of the Japan Academy, Series A, Mathematical Sciences

Collapsing K3 surfaces and Moduli compactification

Yuji Odaka and Yoshiki Oshima

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

First available in Project Euclid: 29 September 2018

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Mathematical Reviews number (MathSciNet)

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]

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


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.

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