Lectures on Resolution of Singularities (AM-166) (Annals of Mathematics Studies, 166) by János Kollár (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “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”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”The book will be an invaluable tool not only for graduate student, but also for algebraic geometers. Mathematicians working in different fields will also enjoy the clarity of the exposition and the wealth of ideas included. This will become, I’m sure, as it happened to most books in this series, one of the classics of modern mathematics.”—Paul Blaga, Mathematica About the Author János Kollár is a professor of Mathematics at Princeton University.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Once you learn Hartshorne’s Algebraic Geometry, it is a good place to see the applications. Moreover, the book contains a lot of elegant examples which are very classical. It is edible for the classical flavor.

⭐Resolution is now a very important part in algebraic geometry, because algebraic geometors inavoidly will meet singularities. Prof. Kollar gave a lot of examples and methods of resolving singularities in curves and surfaces cases. It’s very readable for graduate students.

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