

Seminar on Geometry of Algebraic Varieties
December 14, 2012 14:00, Moscow, Steklov Mathematical Institute, Room 540 (8 Gubkina)






Donaldson's program to solve the YauTianDonaldson conjecture from an algebraic viewpoint
Jesus Martinez Garcia^{} 
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Abstract:
Longer than 50 years ago, Eugenio Calabi consider which projective manifolds accept a Kahler metric whose Ricci tensor is constant. In the early 80s, Aubin and Yau proved that we always can find such a metric when the manifold is of general type or CalabiYau. The Fano case was open. Tian and Yau conjectured that, for Fanos, the existence should be equivalent to some sort of stability known as Kstability, a completely algebraic concept. A few years ago Donaldson sketched a programme to prove this conjecture. Recently Chen, Donaldson and Sun announced a proof and, independently, Tian uploaded a complete proof in the ArXiv. In this
talk I will sketch the main ideas behind their proof, illustrating the use of a modified version of Tian's alphainvariant, for the case of del Pezzo surfaces.

