Conferencia de

Bernd Schober (Leibniz Universität Hannover)

Fecha y Lugar: Miércoles 9 de marzo, 12:00, SEMINARIO A125 DE LA FAC. DE CIENCIAS

Title: Resolution of singularities in dimension two following Cossart--Jannsen--Saito

Abstract: In 2009 Cossart--Jannsen--Saito gave a proof for canonical resolution of singularities for excellent schemes of dimension at most two which is based on classical work by Hironaka for hypersurfaces. As a special feature the approach determines the centers of the upcoming blow-ups purely by the geometry of the maximal singular locus and the history of the resolution process. The finiteness of the constructed sequence of blow-ups is then shown by contradiction -- and not by using a strictly decreasing invariant measuring the complexity of the singularity. In my talk I explain the strategy of Cossart--Jannsen--Saito and present the key ingredients for the construction of an invariant $ iota $ which can be associated to it. Finally, I will give the ideas for the proof that $ iota $ strictly decreases after each blow-up following the strategy.