Localizing the Donaldson–Futaki invariant.

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. [ABSTRACT FROM AUTHOR]