Table of Contents

Introduction Non-singularity and resolution of singularities Curve singularities Resolution type theorems Surface singularities Resolution of singularities in characteristic zero Resolution of surfaces in positive characteristic Local uniformization and resolution of surfaces Ramification of valuations and simultaneous resolution Smoothness and non-singularity Bibliography Index.

Reviews

“This book, based on the author’s lectures at the University of Missouri and the Chennai Mathematics Institute, presents a purely algebraic approach to the resolution of singularities. …requires the level of knowledge of algebraic geometry and commutative algebra usually covered in an introductory graduate-level course. … It is suitable for anyone who wants to learn about the algebraic theory of resolution of singularities and read a reasonably short proof of the existence of resolutions in characteristic zero.”
-- Bulletin of the London Mathematical Society