Marc Levine (Uni Duisburg-Essen)
Wednesday, November 29, 2017 - 13:00
HU, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin-Adlershof, 1.114, 1. Stock
Forschungsseminar "Algebraische Geometrie"
Prof. Dr. Gavril Farkas, Prof. Dr. Bruno Klingler
As part of a program to develop an enumerative geometry with values in quadratic forms, we would like to have a practical calculus for suitable characteristic classes of vector bundles. One promising setting is via the theory of Pontryagin/Euler classes the cohomology of the sheaf of Witt groups. We describe the main points of this calculus: the SL_2-splitting principle of Ananyevskiy, an extension to a splliting principle for reduction to the normaliser of the torus in SL_2, and the computation of Pontryagin/Euler classes of symmetric powers of SL_2-bundles. As an application, we compute the quadratic form ``counting’’ the lines on a smooth hypersurface of degree 2d-1 in P^{d+1}.
submitted by Kristina Schulze (schulze@math.hu-berlin.de)