We use the equivariant localization formula to prove that the Donaldson-Futaki invariant of a compact smooth (K{\"a}hler) 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.
The Donaldson-Futaki invariant for sequences of test configurations
The Kähler-Ricci flow and quantitative bounds for Donaldson-Futaki invariants of optimal degenerations
Odd type generalized complex structures on 4-manifolds
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