Resolution of Singularities

Saturday, April 14, 2007 - 9:00am - 10:30am
EE/CS 3-180
Herwig Hauser (Leopold-Franzens Universität Innsbruck)
This is a spectacular subject, both by its many applications
and its intricate proof. We describe in the talk the main ideas
(after Zariski, Hironaka, Abhyankar and various other people)
how to use blowups for the resolution of singular varieties,
and how to build up an induction procedure to choose at each
step of the resoluton process the center of the next blowup and
to show that the singularities have improved after blowup. The
key constructions and phenomena are illustrated by
visualizations of surface singularities.

As the talk will give mostly the intuitive ideas, we would like
to refer the interested reader for details to three notes we
have written on the subject. There, also quite complete lists
of other references can be found.

The three references to my talk are on my web-site