K3曲面的塌缩与模紧化

Pub Date : 2018-05-04 DOI:10.3792/pjaa.94.81

Y. Odaka, Y. Oshima

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引用次数: 13

摘要

本文总结了我们的工作[OO]，该工作为Ricci-flat Kahler度量的坍缩提供了一个明确的全局模理论框架，并将其用于研究K3曲面的情况。例如，它允许我们讨论它们在任何序列上的Gromov-Hausdorff极限，这些序列甚至不一定是“最大退化”的。在K3曲面作为副产物的情况下，我们的结果也给出了kontsevic - soibelman [KS04，猜想1](参见，[GW00，猜想6.2])的证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Collapsing K3 surfaces and Moduli compactification

This note is a summary of our work [OO] which provides an explicit and global moduli-theoretic framework for the collapsing of Ricci-flat Kahler 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 [KS04, Conjecture 1] (cf., [GW00, Conjecture 6.2]) in the case of K3 surfaces as a byproduct.

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