Constant scalar curvature Kähler metrics on fibred complex surfaces
Constant scalar curvature Kähler metrics on fibred complex surfaces
复制标题
纤维复杂表面上的恒定标量曲率凯勒度量
DOI：
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发表时间：
2004
期刊：
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通讯作者：
J. Fine
中科院分区：
文献类型：
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作者：
J. Fine
本文在某些紧致复曲面上找到常数量曲率的Kahler度量。考虑的表面是那些承认一个全纯淹没曲线，与纤维的亏格至少2。证明是通过绝热极限。一个近似的解决方案是构造出的双曲度量的纤维和一个大的倍数，一定的度量的基础上。一个依赖于参数的反函数定理，然后扰动的近似解决方案，真正的解决方案在同一上同调类。这些论点也适用于某些高维的Kahler流形。
This article finds constant scalar curvature Kahler metrics on certain compact complex surfaces. The surfaces considered are those admitting a holomorphic submersion to a curve, with fibres of genus at least 2. The proof is via an adiabatic limit. An approximate solution is constructed out of the hyperbolic metrics on the fibres and a large multiple of a certain metric on the base. A parameter-dependent inverse function theorem is then used to perturb the approximate solution to a genuine solution in the same cohomology class. The arguments also apply to certain higher dimensional fibred Kahler manifolds.