大上同调类的Mabuchi几何

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-04-27 DOI:10.1515/crelle-2023-0019

Mingchen Xia

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引用次数: 0

摘要

设X是一个紧的Kähler流形。固定一个具有光滑表示θ的大{(1,1)(1,1)}-上同调类α。我们研究了每一个p≥1 p {\geq}{ 1的有限能量Kähler位能}{{的空间(}}{p}{²(X， θ) }{\mathcal{E}}{ ^p(X, }{}{\theta}{)}。我们{在不使用Finsler几何和不{求解}}monge - ampement - re型方程的情况下定义了度规d p d＿p。此构造泛化了{为示例类定义的通常的{pd＿p}} -度量。

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Mabuchi geometry of big cohomology classes

Abstract Let X be a compact Kähler manifold. Fix a big ( 1 , 1 ) {(1,1)} -cohomology class α with smooth representative θ. We study the spaces ℰ p ⁢ ( X , θ ) {\mathcal{E}^{p}(X,\theta)} of finite energy Kähler potentials for each p ≥ 1 {p\geq 1} . We define a metric d p {d_{p}} without using the Finsler geometry nor solving Monge–Ampère-type equations. This construction generalizes the usual d p {d_{p}} -metric defined for an ample class.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.