Constant scalar curvature Kähler metrics on ramified Galois coverings

IF 1.2 1区数学 Q1 MATHEMATICS

Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-10-04 DOI:10.1515/crelle-2023-0026

C. Arezzo, A. Della Vedova, Yalong Shi

引用次数: 1

Abstract

Abstract We give sufficient conditions for the existence of Kähler–Einstein and constant scalar curvature Kähler (cscK) metrics on finite ramified Galois coverings of a cscK manifold in terms of cohomological conditions on the Kähler classes and the branching divisor. This result generalizes previous work on Kähler–Einstein metrics by Li and Sun [C. Li and S. Sun, Conical Kähler–Einstein metrics revisited, Comm. Math. Phys. 331 2014, 3, 927–973], and extends Chen–Cheng’s existence results for cscK metrics in [X. Chen and J. Cheng, On the constant scalar curvature Kähler metrics (II)—Existence results, J. Amer. Math. Soc. 34 2021, 4, 937–1009].

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分支伽罗瓦覆盖上的常数标量曲率Kähler度量

摘要利用Kähler类和分支除数上的上同调条件，给出了cscK流形有限分支伽罗瓦覆盖上Kähler-Einstein和常数标量曲率Kähler (cscK)度量存在的充分条件。这一结果推广了Li和Sun先前关于Kähler-Einstein指标的工作[C]。Li和S. Sun，圆锥体Kähler-Einstein指标重新审视，通讯数学。[j]，并推广了陈诚关于cscK测度的存在性结果[j] .物理学报，2014,39(3):927-973。陈建军，关于常数标量曲率Kähler度量(II) -存在性结果，j。数学。[j].中国生物医学工程学报，2016,31(4):937-1009。

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来源期刊

Journal fur die Reine und Angewandte Mathematik 数学-数学

CiteScore

2.50

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of Crelle"s Journal. In the almost 180 years of its existence, Crelle"s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals. It belongs to the very top mathematics periodicals, as listed in ISI"s Journal Citation Report.