| 概要 | Resolution of singularities in characteristic zero can be
solved using the induction via the notion of a hypersurface of maximal
contact (h.m.c.). In positive characteristic, on the other hand,
the lack of a h.m.c. and hence the lack of a simple inductive scheme
on dimension have been the big obstacle. Recently some approaches have
appeared in search of a new inductive scheme.
We will discuss our approach, a joint work with Hiraku Kawanoue at RIMS.
We present an algorithm, which can be successfully carried out up to
dimension 3, following the recent method of Benito-Villamayor.
This provides a simpler and algorithmic proof to resolution of
singularities of a surface embedded in a smooth 3-dimensional space,
a classical theorem of Abhyankar and Hironaka. |