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Extremal metrics and K-stability

Gábor Székelyhidi
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Abstract

We propose an algebraic geometric stability criterion for a polarised variety to admit an extremal Kaehler metric. This generalises conjectures by Yau, Tian and Donaldson which relate to the case of Kaehler-Einstein and constant scalar curvature metrics. We give a result in geometric invariant theory that motivates this conjecture, and an example computation that supports it.

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Gábor Székelyhidi. 2007-04-02. Extremal metrics and K-stability. https://arxiv.org/abs/math/0410401

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