Compactification of certain Kähler manifolds with nonnegative Ricci curvature

Gang Liu

doi:10.1016/j.aim.2021.107652

Compactification of certain Kähler manifolds with nonnegative Ricci curvature

Gang Liu

School of Mathematical Sciences

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

6 Scopus citations

Abstract

We prove compactification theorems for some complete Kähler manifolds with nonnegative Ricci curvature. Among other things, we prove that a complete non-compact Ricci-flat Kähler manifold with maximal volume growth and quadratic curvature decay is a crepant resolution of a normal affine algebraic variety. Furthermore, such an affine variety degenerates in two steps to the unique metric tangent cone at infinity.

Original language	English
Article number	107652
Journal	Advances in Mathematics
Volume	382
DOIs	https://doi.org/10.1016/j.aim.2021.107652
State	Published - 14 May 2021

Keywords

Compactification
Kähler manifolds
Ricci curvature

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10.1016/j.aim.2021.107652

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title = "Compactification of certain K{\"a}hler manifolds with nonnegative Ricci curvature",

abstract = "We prove compactification theorems for some complete K{\"a}hler manifolds with nonnegative Ricci curvature. Among other things, we prove that a complete non-compact Ricci-flat K{\"a}hler manifold with maximal volume growth and quadratic curvature decay is a crepant resolution of a normal affine algebraic variety. Furthermore, such an affine variety degenerates in two steps to the unique metric tangent cone at infinity.",

keywords = "Compactification, K{\"a}hler manifolds, Ricci curvature",

author = "Gang Liu",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2021",

month = may,

day = "14",

doi = "10.1016/j.aim.2021.107652",

language = "英语",

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T1 - Compactification of certain Kähler manifolds with nonnegative Ricci curvature

AU - Liu, Gang

PY - 2021/5/14

Y1 - 2021/5/14

N2 - We prove compactification theorems for some complete Kähler manifolds with nonnegative Ricci curvature. Among other things, we prove that a complete non-compact Ricci-flat Kähler manifold with maximal volume growth and quadratic curvature decay is a crepant resolution of a normal affine algebraic variety. Furthermore, such an affine variety degenerates in two steps to the unique metric tangent cone at infinity.

AB - We prove compactification theorems for some complete Kähler manifolds with nonnegative Ricci curvature. Among other things, we prove that a complete non-compact Ricci-flat Kähler manifold with maximal volume growth and quadratic curvature decay is a crepant resolution of a normal affine algebraic variety. Furthermore, such an affine variety degenerates in two steps to the unique metric tangent cone at infinity.

KW - Compactification

KW - Kähler manifolds

KW - Ricci curvature

UR - https://www.scopus.com/pages/publications/85101529433

U2 - 10.1016/j.aim.2021.107652

DO - 10.1016/j.aim.2021.107652

M3 - 文章

AN - SCOPUS:85101529433

SN - 0001-8708

VL - 382

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 107652

ER -

Compactification of certain Kähler manifolds with nonnegative Ricci curvature

Abstract

Keywords

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