The Kähler-Ricci flow on log canonical pairs of general type

Chang Li; Liangming Shen; Tao Zheng

doi:10.1016/j.jfa.2023.109984

The Kähler-Ricci flow on log canonical pairs of general type

Chang Li
, Liangming Shen
, Tao Zheng^*

^*此作品的通讯作者

数学科学学院

School of Mathematics
Beijing Institute of Technology

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

We generalize existence results of the Kähler-Ricci flow in [10] to log canonical pairs. We show that if the initial data is in L^∞ the Kähler-Ricci flow simultaneously develops the conical and cusp singularities along the regular part of the corresponding pair divisors. Furthermore we could show that the normalized Kähler-Ricci flow converges to the singular Kähler-Einstein metric inside the ample locus of K_X+Δ if the log canonical pair is of general type.

源语言	英语
文章编号	109984
期刊	Journal of Functional Analysis
卷	285
期	4
DOI	https://doi.org/10.1016/j.jfa.2023.109984
出版状态	已出版 - 15 8月 2023

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title = "The K{\"a}hler-Ricci flow on log canonical pairs of general type",

abstract = "We generalize existence results of the K{\"a}hler-Ricci flow in [10] to log canonical pairs. We show that if the initial data is in L∞ the K{\"a}hler-Ricci flow simultaneously develops the conical and cusp singularities along the regular part of the corresponding pair divisors. Furthermore we could show that the normalized K{\"a}hler-Ricci flow converges to the singular K{\"a}hler-Einstein metric inside the ample locus of KX+Δ if the log canonical pair is of general type.",

keywords = "Big and nef, K{\"a}hler-Ricci flow, Log canonical pair",

author = "Chang Li and Liangming Shen and Tao Zheng",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier Inc.",

year = "2023",

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AU - Li, Chang

AU - Shen, Liangming

AU - Zheng, Tao

PY - 2023/8/15

Y1 - 2023/8/15

N2 - We generalize existence results of the Kähler-Ricci flow in [10] to log canonical pairs. We show that if the initial data is in L∞ the Kähler-Ricci flow simultaneously develops the conical and cusp singularities along the regular part of the corresponding pair divisors. Furthermore we could show that the normalized Kähler-Ricci flow converges to the singular Kähler-Einstein metric inside the ample locus of KX+Δ if the log canonical pair is of general type.

AB - We generalize existence results of the Kähler-Ricci flow in [10] to log canonical pairs. We show that if the initial data is in L∞ the Kähler-Ricci flow simultaneously develops the conical and cusp singularities along the regular part of the corresponding pair divisors. Furthermore we could show that the normalized Kähler-Ricci flow converges to the singular Kähler-Einstein metric inside the ample locus of KX+Δ if the log canonical pair is of general type.

KW - Big and nef

KW - Kähler-Ricci flow

KW - Log canonical pair

UR - https://www.scopus.com/pages/publications/85156193679

U2 - 10.1016/j.jfa.2023.109984

DO - 10.1016/j.jfa.2023.109984

M3 - 文章

AN - SCOPUS:85156193679

SN - 0022-1236

VL - 285

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 4

M1 - 109984

ER -

The Kähler-Ricci flow on log canonical pairs of general type

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