Lectures on Resolution of Singularities

Resolution of singularities is a powerful and frequently used tool in algebraic geometry. In this book, János Kollár provides a comprehensive treatment of the characteristic 0 case. He describes more than a dozen proofs for curves, many based on the original papers of Newton, Riemann, and Noether. Kollár goes back to the original sources and presents them in a modern context. He addresses three methods for surfaces, and gives a self-contained and entirely elementary proof of a strong and functorial resolution in all dimensions. Based on a series of lectures at Princeton University and written in an informal yet lucid style, this book is aimed at readers who are interested in both the historical roots of the modern methods and in a simple and transparent proof of this important theorem.

"People are already using this book. I am using this book now. I expect it will be used well into the future."---Dan Abramovich, Mathematical Reviews

"Throughout his lectures, Kollar uses plenty of motivations and examples, and the text is very readable. Any graduate student or mathematicians who wishes to learn about the subject would be well-served to use this book as a starting point."---Darren Glass, MAA Review