Extremal Kaehler Metrics and Kaehler-Ricci Flow

seminar: A packing problem for automorphisms of Riemann surfaces and the slope of Kodaira fibrations

speaker: Fabrizio Catanese (Universität Bayreuth)

abstract: In the year 1967 Kodaira found a counterexample to the multiplicativity of the signature for fibre bundles, constructing an algebraic surface with a fibration over a curve which is a differentiable but not a holomorphic fibre bundle. In his honour such fibrations are called Kodaira fibrations. The measure of the positivity of the signature is given by the slope \nu, the ratio between the two Chern numbers, c12 c2. One has 2 < \nu < 3, and a question asked by Le Brun is how close can \nu get to 3. The examples of Kodaira have slope 73. I will report on joint work with Soenke Rollenske, showing the existence of a special type of Kodaira fibrations which are easier to construct and for which we can determine explicitly the moduli space. We construct new examples with slope \nu = 2 + 23 = 83, using algebraic curves with many automorphisms, and we construct rigid Kodaira fibred surfaces. I will discuss some conjectures and questions, in particular an interesting connection with a packing problem in group theory. In the end I will describe some results concerning the moduli spaces of these surfaces.

timetable:
Mon 10 Mar, 11:15 - 12:15, Sala Conferenze Centro De Giorgi
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