The Kähler-Ricci flow and quantitative bounds for Donaldson-Futaki invariants of optimal degenerations
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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.References
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Additional Information
- Ryosuke Takahashi
- Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
- MR Author ID: 1164292
- Email: tryosuke@kurims.kyoto-u.ac.jp
- 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
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 3527-3536
- MSC (2010): Primary 53C55; Secondary 14L24
- DOI: https://doi.org/10.1090/proc/15004
- MathSciNet review: 4108858