Algebraic Varieties: Minimal Models and Finite Generation (Cambridge Studies in Advanced Mathematics) - Hardcover

Kawamata, Yujiro

Hardcover

ISBN 10: 1009344676 ISBN 13: 9781009344678

Publisher: Cambridge University Press, 2024

Synopsis

The finite generation theorem is a major achievement in modern algebraic geometry. Based on the minimal model theory, it states that the canonical ring of an algebraic variety defined over a field of characteristic 0 is a finitely generated graded ring. This graduate-level text is the first to explain this proof. It covers the progress on the minimal model theory over the last 30 years, culminating in the landmark paper on finite generation by Birkar‒Cascini‒Hacon‒McKernan. Building up to this proof, the author presents important results and techniques that are now part of the standard toolbox of birational geometry, including Mori's bend-and-break method, vanishing theorems, positivity theorems, and Siu's analysis on multiplier ideal sheaves. Assuming only the basics in algebraic geometry, the text keeps prerequisites to a minimum with self-contained explanations of terminology and theorems.

About this title

About the Author

Yujiro Kawamata is a professor at the University of Tokyo. He is the recipient of various prizes and awards, including the Mathematical Society of Japan Autumn award (1988), the Japan Academy of Sciences award (1990), ICM speaker (1990), and ISI Highly Cited Researcher (2001).

Edition details

• Publisher: Cambridge University Press
• Publication date: 2024
• Language: English
• ISBN 10: 1009344676
• ISBN 13: 9781009344678
• Binding: Hardcover
• Number of pages: 262