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

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

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

Access to Document

10.1090/proc/15004

Cite this

@article{797f487952354401960cfd378e76515a,

title = "The K{\"a}hler-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 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.",

author = "Ryosuke Takahashi",

note = "Publisher Copyright: {\textcopyright} 2020 American Mathematical Society",

year = "2020",

month = aug,

doi = "10.1090/proc/15004",

language = "English",

volume = "148",

pages = "3527--3536",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "8",

}

TY - JOUR

T1 - The Kähler-Ricci flow and quantitative bounds for Donaldson-Futaki invariants of optimal degenerations

AU - Takahashi, Ryosuke

PY - 2020/8

Y1 - 2020/8

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=85090797050&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85090797050&partnerID=8YFLogxK

U2 - 10.1090/proc/15004

DO - 10.1090/proc/15004

M3 - Article

AN - SCOPUS:85090797050

VL - 148

SP - 3527

EP - 3536

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 8

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this