The Kähler-Ricci flow and quantitative bounds for Donaldson-Futaki invariants of optimal degenerations

Abstract

We establish a lower bound for the Donaldson-Futaki invariant of optimal degenerations produced by the Kähler-Ricci flow in terms of the greatest Ricci lower bound on arbitrary Fano manifolds. As an application, we can generalize the finiteness of the Futaki invariants on Kähler-Ricci solitons obtained by Guo-Phong-Song-Sturm to the space of all Fano manifolds. Also, we discuss the relation to Hisamoto's inequality for the infimum of the $H$-functional.

arXiv comment11 pages, final version, to appear in Proc. Amer. Math. Soc

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