Collapsing K3 surfaces and Moduli compactification
Collapsing K3 surfaces and Moduli compactification
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DOI：
10.3792/pjaa.94.81
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发表时间：
2018-05
期刊：
影响因子：
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通讯作者：
Y. Odaka;Y. Oshima
中科院分区：
文献类型：
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作者：
Y. Odaka;Y. Oshima
本文是我们工作的总结[OO]，它为Ricci平坦Kahler度量的崩溃提供了一个明确的和全局的模理论框架，我们用它来研究特别是K3曲面的情况。例如，它允许我们讨论他们的Gromov-Hausdorff极限沿着任何序列，这甚至不一定是“最大退化”。我们的结果还证明了Kontsevich-Soibelman [KS 04，猜想1]（参见，[GW00，猜想6.2]）在K3表面作为副产物的情况下。
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.