复数空间的非阿基米德理论和 cscK 问题

arXiv - MATH - Differential Geometry Pub Date : 2024-09-10 DOI:arxiv-2409.06221

Pietro Mesquita-Piccione

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引用次数: 0

摘要

在本文中，我们为非必然代数复数空间发展了伯科维奇分析法。我们将这一理论推广到任意紧凑的 K\"ahler 流形上，证明了 K-stability 的更强版本意味着存在唯一的常卡尔曲率 K\"ahler 度量。

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A non-Archimedean theory of complex spaces and the cscK problem

In this paper we develop an analogue of the Berkovich analytification for non-necessarily algebraic complex spaces. We apply this theory to generalize to arbitrary compact K\"ahler manifolds a result of Chi Li, proving that a stronger version of K-stability implies the existence of a unique constant scalar curvature K\"ahler metric.

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arXiv - MATH - Differential Geometry

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