Algebraic Varieties

Minimal Models and Finite Generation

Yujiro Kawamata (University of Tokyo), Chen Jiang (Fudan University, Shanghai)

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English

Cambridge University Press
27 June 2024

Algebra; Algebraic geometry

Series: Cambridge Studies in Advanced Mathematics

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.

By: Yujiro Kawamata (University of Tokyo)
Translated by: Chen Jiang (Fudan University Shanghai)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 229mm, Width: 152mm, Spine: 16mm
Weight: 539g
ISBN: 9781009344678
ISBN 10: 1009344676
Series: Cambridge Studies in Advanced Mathematics
Pages: 262
Publication Date: 27 June 2024
Audience: College/higher education , Further / Higher Education
Format: Hardback
Publisher's Status: Active

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).