For any Fano manifold, the Donaldson-Futaki invariant of its optimal degeneration is bounded below by -(1-R(X))/R(X) nV, where R(X) is the greatest Ricci lower bound.
Campana \'e retionnelle des vari\'et\'es de Fano
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The K\"ahler-Ricci flow and quantitative bounds for Donaldson-Futaki invariants of optimal degenerations
For any Fano manifold, the Donaldson-Futaki invariant of its optimal degeneration is bounded below by -(1-R(X))/R(X) nV, where R(X) is the greatest Ricci lower bound.