A self-contained introduction to minimal model theory and the finite generation theorem of the canonical ring of algebraic varieties.
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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).
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Hardcover. Zustand: new. Hardcover. 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 BirkarCasciniHaconMcKernan. 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. The first graduate-level introduction to the finite generation theorem of the canonical ring, a major achievement of modern algebraic geometry. Largely self-contained, this text explains the basics of minimal model theory, covering all the progress of the last three decades and assuming only the basics in algebraic geometry. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9781009344678
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Hardback. Zustand: New. 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. Bestandsnummer des Verkäufers LU-9781009344678
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