Lectures on Resolution of Singularities (AM-166) (Annals of Mathematics Studies (166))

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.

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.

Dan Abramovich - Mathematical Reviews

People are already using this book. I am using this book now. I expect it will be used well into the future.

"Resolution of singularities is a powerful and frequently used tool in algebraic geometry. In this book, Janos Kollar 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. Kollar 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."--Publisher's description Resolution of singularities is a powerful and frequently used tool in algebraic geometry. This book provides a comprehensive treatment of the characteristic 0 case. It describes more than a dozen proofs for curves, many based on the original papers of Newton, Riemann, and Noether Contents Introduction Chapter 1. Resolution for Curves Chapter 2. Resolution for Surfaces Chapter 3. Strong Resolution in Characteristic Zero Bibliography Index A complex algebraic variety X is a subset of complex affine n-space Cn or of complex projective n-space CPn defined by polynomial equations.