On the geometry of moduli spaces
On the geometry of moduli spaces
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关于模空间的几何
DOI：
10.1007/bf01168833
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发表时间：
1985
影响因子：
0.6
通讯作者：
G. Schumacher
中科院分区：
文献类型：
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作者：
G. Schumacher
在c1 <0的紧复流形和c1=0的极化紧Kähler流形的模空间上构造了一个Kähler度规，这是对Petersson-Well度规的推广。它是由根据Calabi-Yau定理存在的纤维上Kähler-Einstein度量的变化引起的。我们在极化环面和辛流形的模空间上计算了上述度规。它是西格尔上半空间上的马斯度规和III型对称空间上的伯格曼度规。特别地，它是负曲率Kähler-Einstein。
We construct a Kähler metric on the moduli spaces of compact complex manifolds with c1,<0 and of polarized compact Kähler manifolds with c1=0, which is a generalization of the Petersson-Well metric. It is induced by the variation of the Kähler-Einstein metrics on the fibers that exist according to the Calabi-Yau theorem. We compute the above metric on the moduli spaces of polarized tori and symplectic manifolds. It turns out to be the Maaß metric on the Siegel upper half space and the Bergmann metric on a symmetric space of type III resp. In particular it is Kähler-Einstein with negative curvature.