Ivan Cheltsov

Stable and unstable del Pezzo surfaces

Yau-Tian-Donaldson conjecture, recently proved by Chen, Donaldson and Sun, says that a Fano manifold is Kahler-Einstein if and only if it is K-stable. Its stronger form, still open, says that a polarized manifold (M,L) is K-stable if and only if M admits a constant scalar curvature with Kahler class in L. In this talk, I will describe K-stability of ample line bundles on smooth del Pezzo surfaces (two-dimensional Fano manifolds). I will show how to apply recent result of Dervan to prove K-stability and how to use flop-version of Ross and Thomas's obstruction to prove instability.

The talk is based on my joint work with Jesus Martinez-Garcia (Johns Hopkins University, Baltimore, USA).

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