Constant scalar curvature Kaehler metrics on fibred complex surfaces

December 7th, 2004 at 15:15 in HG G43 (HWZ)

Given by: Joel Fine (Imperial College, London)

Abstract: In the first half of the talk I will motivate the search for constant scalar curvature Kaehler metrics on arbitrary smooth varieties. The main motivation comes from the conjectural equivalence of the existence of such a metric with the stability of the underlying variety (an analogue of the Hitchin-Kobayashi correspondence). In the second half, I will explain how to prove the existence of such a metric on a complex surface which fibres over a curve, with all fibres smooth and of genus at least 2. The method goes via an adiabatic limit, and a parameter dependent implicit function theorem (both of which I will explain assuming no prior knowledge).