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Oberseminar SoSe 2009 Zusammenfassung des Vortrags von A. Frühbis-Krüger

Desingularization in positive characteristic, kangaroo points and obstacles to generalizing the Hauser-Wagner approach to dimension 3

H. Hauser identified the main obstacles to desingularization in positive characteristic as polynomials with a very special structure of the tangent cone. The Hauser-Wagner approach to resolution of surface singularities is based on this explicit knowledge and uses it to prove the fact that with slight modifications the usual resolution invariant (of the characteristic zero case) also decreases in the long run in positive characteristic. A generalization of this approach to dimension 3, preferably by use of inductive arguments, would shed some light on possible approaches to the general task of desingularization in positive characteristic. After recalling the Hauser-Wagner approach, the talk will focus on problems and tasks arising in the quest to generalize this approach.