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arXiv · 1909.02452

The K\"ahler-Ricci flow and quantitative bounds for Donaldson-Futaki invariants of optimal degenerations

Ryosuke Takahashi
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Abstract

We establish a lower bound for the Donaldson-Futaki invariant of optimal degenerations produced by the K\"ahler-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 K\"ahler-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.

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Ryosuke Takahashi. 2019-09-05. The K\"ahler-Ricci flow and quantitative bounds for Donaldson-Futaki invariants of optimal degenerations. https://arxiv.org/abs/1909.02452

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