DEGENERATION OF CALABI-YAU MANIFOLD WITH WEIL-PETERSSON METRIC
DEGENERATION OF CALABI-YAU MANIFOLD WITH WEIL-PETERSSON METRIC
复制标题
具有Weil-Petersson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;Y. Hayakawa
Koiso是第一个在更高维度上引入Weil-Petersson度量的人。Tian证明了Calabi-Yau n-流形的模空间自然具有Weil-Petersson度量。在本文中，我们专注于确定退化的中央纤维是在有限的距离相对于Weil-Petersson度量。首先得到了极限混合Hodge结构的一个简单条件，该条件是到中心纤维的Weil-Petersson距离有限的充要条件。这个问题已经在物理学文献中提出，但没有得到广泛的分析。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充要条件.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。
Koiso was first to introduce the Weil-Petersson metric in higher dimension. Tian showed that a moduli space of Calabi-Yau n-manifolds comes naturally with Weil-Petersson metric. In this paper we focus on determining for which degenerations the central fibre is at finite distance with respect to the Weil-Petersson metric. First we obtain a simple condition on the limiting mixed Hodge structure which is a necessary and sufficient condition for finite Weil-Petersson distance to the central fibre. This issue has been raised in the Physics literature but not extensively analyzed there. Then we combine the result with the canonical mixed Hodge structure of the central fibre and obtain a simple cohomological necessary and sufficient 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.