
Algebraic Varieties: Minimal Models and Finite Generation
Minimal Models and Finite Generation
Yujiro Kawamata(Author)
Cambridge University Press
Published on 27. June 2024
Book
Hardback
262 pages
978-1-009-34467-8 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Illustrations
Worked examples or Exercises
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 19 mm
Weight
535 gr
ISBN-13
978-1-009-34467-8 (9781009344678)
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Schweitzer Classification
Persons
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).
Content
Preface; 1. Introduction; 2. Algebraic varieties with boundaries; 3. The minimal model program; 4. The finite generation theorem; Bibliography; Index.