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


Author: Ryosuke Takahashi
Journal: Proc. Amer. Math. Soc. 148 (2020), 3527-3536
MSC (2010): Primary 53C55; Secondary 14L24
DOI: https://doi.org/10.1090/proc/15004
Published electronically: March 25, 2020
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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.


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Additional Information

Ryosuke Takahashi
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
Email: tryosuke@kurims.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/proc/15004
Received by editor(s): September 12, 2019
Received by editor(s) in revised form: December 18, 2019
Published electronically: March 25, 2020
Communicated by: Jia-Ping Wang
Article copyright: © Copyright 2020 American Mathematical Society