The existence of the Kähler–Ricci soliton degeneration

Harold Blum; Yuchen Liu; Chenyang Xu; Ziquan Zhuang

doi:10.1017/fmp.2023.5

The existence of the Kähler–Ricci soliton degeneration

Harold Blum, Yuchen Liu, Chenyang Xu, Ziquan Zhuang

Mathematics

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

4 Scopus citations

Abstract

We prove an algebraic version of the Hamilton-Tian conjecture for all log Fano pairs. More precisely, we show that any log Fano pair admits a canonical two-step degeneration to a reduced uniformly Ding stable triple, which admits a Kähler-Ricci soliton when the ground field.

Original language	English (US)
Article number	e9
Journal	Forum of Mathematics, Pi
Volume	11
DOIs	https://doi.org/10.1017/fmp.2023.5
State	Published - Mar 10 2023

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Statistics and Probability
Mathematical Physics
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1017/fmp.2023.5

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title = "The existence of the K{\"a}hler–Ricci soliton degeneration",

abstract = "We prove an algebraic version of the Hamilton-Tian conjecture for all log Fano pairs. More precisely, we show that any log Fano pair admits a canonical two-step degeneration to a reduced uniformly Ding stable triple, which admits a K{\"a}hler-Ricci soliton when the ground field.",

author = "Harold Blum and Yuchen Liu and Chenyang Xu and Ziquan Zhuang",

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T1 - The existence of the Kähler–Ricci soliton degeneration

AU - Blum, Harold

AU - Liu, Yuchen

AU - Xu, Chenyang

AU - Zhuang, Ziquan

PY - 2023/3/10

Y1 - 2023/3/10

N2 - We prove an algebraic version of the Hamilton-Tian conjecture for all log Fano pairs. More precisely, we show that any log Fano pair admits a canonical two-step degeneration to a reduced uniformly Ding stable triple, which admits a Kähler-Ricci soliton when the ground field.

AB - We prove an algebraic version of the Hamilton-Tian conjecture for all log Fano pairs. More precisely, we show that any log Fano pair admits a canonical two-step degeneration to a reduced uniformly Ding stable triple, which admits a Kähler-Ricci soliton when the ground field.

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DO - 10.1017/fmp.2023.5

M3 - Article

AN - SCOPUS:85150069558

SN - 2050-5086

VL - 11

JO - Forum of Mathematics, Pi

JF - Forum of Mathematics, Pi

M1 - e9

ER -

The existence of the Kähler–Ricci soliton degeneration

Abstract

All Science Journal Classification (ASJC) codes

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