Degenaration of Calabi-Yau Manifold with W-P Metric
Degenaration of Calabi-Yau Manifold with W-P Metric
复制标题
具有 W-P 度量的 Calabi-Yau 流形的退化
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
Y. Hayakawa
中科院分区：
文献类型：
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作者：
Y. Hayakawa
在本文中，我们专注于确定退化的中央纤维是在有限距离的Weil-Petersson度量。得到了极限混合Hodge结构的一个简单条件。然后将所得结果与中心纤维的正则混合Hodge结构相结合，得到了中心纤维在有限距离上的一个简单的上同调条件。作为推论，我们证明了具有简单节点的中心纤维在有限距离处。这个问题已经在物理学文献中提出，包括最近所谓的“无质量黑洞”的发展。
In this paper we focus on determining for which degenerations the central fibre is at finite distance with respect to Weil-Petersson metric. We obtain a simple condition on the limiting mixed Hodge structure. Then we combine the result with the canonical mixed Hodge structure of the central fibre and obtain a simple cohomological condition for the central fibre to be at finite distance. As a corollary, we prove that a central fibre with simple nodes is at finite distance. This issue has been raised in the Physics literature including the recent development of so-called "mass-less black holes".