Extremal metrics and K-stability

Details Extremal metrics and K-stability Extremal metrics and K-stability

2004-10-18

arxiv.org/abs/math/0410401v3

Bull. London Math. Soc. 39 (2007), 76--84

Mathematics

Algebraic Geometry

13 pages, v3: fixed typos

Scientific paper

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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