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Stability in algebraic geometry and its relationship with canonical Kahler metrics (STABILITYMETRICS)
Start date: Oct 1, 2008, End date: Sep 30, 2012 PROJECT  FINISHED 

"The proposal centers around the conjectural equivalence between the existence of special Kahler metrics and stability notions for projective manifolds coming from Geometric Invariant Theory. The stability condition is called K-stability, and the metrics in question are the extremal metrics, which includes the class of Kahler-Einstein metrics and the constant scalar curvature Kahler metrics. The projects will build on what is already known in this area and extend it to apply beyond projective manifolds, as well as connect with other parts of algebraic geometry, notably and stability notions for vector bundles and for pairs in birational geometry."

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