Mabuchi geometry of big cohomology classes

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

引用次数: 0

Abstract

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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大上同调类的Mabuchi几何

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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

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