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Algebraic Varieties: Minimal Models and Finite Generation

Algebraic Varieties: Minimal Models and Finite Generation

Algebraic Varieties: Minimal Models and Finite Generation

Yujiro Kawamata, University of Tokyo
Chen Jiang, Fudan University, Shanghai
No date available
Hardback
9781009344678
Hardback

    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.

    • Explain the basics of minimal model theory for higher dimensional algebraic varieties with boundaries
    • The first book to explain the proof of the finite generation theorem of the canonical ring
    • Includes self-contained explanations of terminology and theorems, assuming only the basics in algebraic geometry

    Product details

    No date available
    Adobe eBook Reader
    9781009344630
    0 pages

    Table of Contents

    • Preface
    • 1. Introduction
    • 2. Algebraic varieties with boundaries
    • 3. The minimal model program
    • 4. The finite generation theorem
    • Bibliography
    • Index.
      Author
    • Yujiro Kawamata , University of Tokyo

      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).

    • Translator
    • Chen Jiang , Fudan University, Shanghai