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

Ryosuke Takahashi

doi:10.1090/proc/15004

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

Ryosuke Takahashi

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 Hfunctional.

Original language	English
Pages (from-to)	3527-3536
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	148
Issue number	8
DOIs	https://doi.org/10.1090/proc/15004
Publication status	Published - Aug 2020
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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abstract = "We establish a lower bound for the Donaldson-Futaki invariant of optimal degenerations produced by the K{\"a}hler-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{\"a}hler-Ricci solitons obtained by Guo-Phong-Song-Sturm to the space of all Fano manifolds. Also, we discuss the relation to Hisamoto{\textquoteright}s inequality for the infimum of the Hfunctional.",

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AB - 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 Hfunctional.

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

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