Extremal metrics on the total space of destabilising test configurations
Lars Martin Sektnan, Cristiano Spotti
TL;DR
This paper constructs extremal K"ahler metrics on the total space of destabilising test configurations, revealing new examples and phenomena such as complex structure jumping along fibers.
Contribution
It introduces a method to produce extremal metrics on destabilising test configurations, expanding the known examples and uncovering novel geometric phenomena.
Findings
Infinite new examples of extremal K"ahler manifolds
Discovery of complex structure jumping along fibers
Demonstration of extremal metrics on destabilising configurations
Abstract
We construct extremal metrics on the total space of certain destabilising test configurations for strictly semistable K\"ahler manifolds. This produces infinitely many new examples of manifolds admitting extremal K\"ahler metrics. It also shows for such metrics a new phenomenon of jumping of the complex structure along fibres.
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Taxonomy
TopicsGeometry and complex manifolds · Mathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows