Collapsing K3 surfaces and Moduli compactification

IF 0.4 4区数学 Q4 MATHEMATICS

Proceedings of the Japan Academy Series A-Mathematical Sciences Pub Date : 2018-05-04 DOI:10.3792/pjaa.94.81

Y. Odaka, Y. Oshima

引用次数: 13

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 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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K3曲面的塌缩与模紧化

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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来源期刊

Proceedings of the Japan Academy Series A-Mathematical Sciences 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The aim of the Proceedings of the Japan Academy, Series A, is the rapid publication of original papers in mathematical sciences. The paper should be written in English or French (preferably in English), and at most 6 pages long when published. A paper that is a résumé or an announcement (i.e. one whose details are to be published elsewhere) can also be submitted. The paper is published promptly if once communicated by a Member of the Academy at its General Meeting, which is held monthly except in July and in August.