ON THE MODULI SPACE OF CALABI-YAU MANIFOLDS
ON THE MODULI SPACE OF CALABI-YAU MANIFOLDS
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论Calabi-Yau流形的模空间
DOI：
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发表时间：
2007
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通讯作者：
Zhiqin Lu
中科院分区：
文献类型：
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作者：
Zhiqin Lu
设X是具有零第一类的单连通紧致Kähler流形，L是X上的充要线丛，这对(X，L)称为极化Calabi-Yau流形。利用Mumford定理，证明了(X，L)(CY模)对的模空间是复变的。局部地，直到有限覆盖，模空间是光滑的(见[20，21])。在M上有一个自然的Kähler度量，称为Weil-Petersson度量。本文总结和讨论了这对偶(M，ωWp)的微分几何，其中ωWp是Weil-Petersson度量的Kähler形式。
Let X be a simply connected compact Kähler manifold with zero first Chern class, and let L be an ample line bundle over X. The pair (X,L) is called a polarized Calabi-Yau manifold. By a theorem of Mumford, the moduli space of the pair (X,L) (CY moduli) exists and is a complex variety. Locally, up to a finite cover, the moduli space is smooth (see [20, 21]). There is a natural Kähler metric, called the Weil-Petersson metric, on M. In this paper, we summarize and discuss the differential geometry of the couple (M, ωWP ), where ωWP is the Kähler form of the Weil-Petersson metric.