松木 謙二 氏(Purdue 大学,米)

内容:
The problem of resolution of singularities simply asks: "Given a variety X over a field k, find a proper birational map from a nonsingular variety to X".
 The celebrated solution by Hironaka in the 1960's in characteristic zero, together with its fame and importance, has established notoriety for its difficult and overwhelming proof. In fact, most of the algebraic geometers have been using the theorem as a ``black box", not to be opened and to be used only according to the specifications of the manufacturer.
 Through the development of constructive algorithms by Bierstone-Milman and Villamayor, however, we saw some substantial simplifications in the 1980-90's. Recently Wlodarczyk brought further simplification, which might put a concise but complete proof into 20 some pages.
 At the talk we would like to present how to resolve singularities at a leisurely pace, following the essential ideas culminating to this easy and elementary proof.