常数量曲率Kähler度量的代数族
Algebraic families of constant scalar curvature Kähler metrics
摘要：
本文给出了一个新的证明，证明了允许Kähler-Einstein度量存在的Fano流形的条件是Zerkiki-开的（只要自同构群是离散的）.这个证明没有使用涉及稳定性的表征。参数涉及的Futaki不变量的估计获得的微分几何的“体积估计”，和变量的代数几何参数的Stoppa。许多想法适用于常数数量曲率凯勒度量。
英文摘要：
We give a new proof of the fact that the condition of a Fano manifold admitting a Kähler-Einstein metric is Zariski-open (provided that the automorphism group is discrete). This proof does not use the characterisation involving stability. The arguments involve estimates of Futaki invariants obtained from a differential-geometric "volume estimate", and variants of the algebro-geometric arguments of Stoppa. Many of the ideas apply to constant scalar curvature Kähler metrics.
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