解析k -半稳定性与局部过壁

IF 0.7 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2025-07-15 DOI:10.1007/s10455-025-10011-6

Lars Martin Sektnan, Carl Tipler

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引用次数: 0

摘要

对于常数标量曲率Kähler流形的一个小的极化变形，在一些上同调消失条件下，我们证明了k -沿附近极化的多稳定性意味着常数标量曲率Kähler度规的存在。在这种情况下，我们将k -多稳定性简化为计算cscK退化上的经典Futaki不变量。我们的结果适用于特定族，并提供了当偏振变化时cscK流形模的局部过壁现象。

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Analytic K-semistability and local wall-crossing

For a small polarised deformation of a constant scalar curvature Kähler manifold, under some cohomological vanishing conditions, we prove that K-polystability along nearby polarisations implies the existence of a constant scalar curvature Kähler metric. In this setting, we reduce K-polystability to the computation of the classical Futaki invariant on the cscK degeneration. Our result holds on specific families and provides local wall-crossing phenomena for the moduli of cscK manifolds when the polarisation varies.

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.