We use the equivariant localization formula to prove that the Donaldson–Futaki invariant of a compact smooth (Kähler) test configuration coincides with the Futaki invariant of the induced action on the central fiber when this fiber is smooth or have orbifold singularities. We also localize the Donaldson–Futaki invariant of the deformation to the normal cone.

中文翻译：

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本地化 Donaldson-Futaki 不变量

我们使用等变局部化公式证明紧凑光滑 (Kähler) 测试配置的 Donaldson-Futaki 不变量与当该纤维光滑或具有 orbifold 奇点时对中心纤维的感应作用的 Futaki 不变量一致。我们还将变形的 Donaldson-Futaki 不变量定位到法向锥。