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Algebraic Varieties: Minimal Models and Finite Generation on Hardback by Yujiro Kawamata
Algebraic Varieties: Minimal Models and Finite Generation on Hardback by Yujiro Kawamata
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Algebraic Varieties: Minimal Models and Finite Generation

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Description

The finite generation theorem is a major achievement of 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 zero 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.

Author Biography:

Yujiro Kawamata is a University 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).
Release date NZ
May 31st, 2024
Audience
  • Postgraduate, Research & Scholarly
Contributor
  • Translated by Chen Jiang
Illustrations
Worked examples or Exercises
Pages
257
ISBN-13
9781009344678
Product ID
38310492

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