Singularitities are known in almost any mathematical theory, and it is always easier if they do not occur. In algebraic geometry, resolution of singularities asks, if one can replace a singular algebraic variety or complex analytic space by a smooth variety or complex manifold which conicides with the starting object in all smooth points. 1964 Hironaka proved that this is possible over the complex numbers and for varieties over a field of characteristic zero. In number theory and arithmetic geometry, varieties over fields of positive characteristic are very important, but resolution is in general not known, except if the dimension is at most 3. I will explain the standard process of resolution, so-called blowups, and willexplain what the problems are for general resolution.
Donnerstag, den 9. Januar 2014 um 17 Uhr c.t. Uhr, in INF 288, HS 2 Donnerstag, den 9. Januar 2014 at 17 Uhr c.t., in INF 288, HS 2
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. A. Schmidt