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Cover: 9781009344678 | Algebraic Varieties | Minimal Models and Finite Generation | Kawamata
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Algebraic Varieties
Minimal Models and Finite Generation
Buch von Yujiro Kawamata
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor
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).
Inhaltsverzeichnis
Preface; 1. Introduction; 2. Algebraic varieties with boundaries; 3. The minimal model program; 4. The finite generation theorem; Bibliography; Index.
Details
Erscheinungsjahr: 2024
Fachbereich: Allgemeines
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
ISBN-13: 9781009344678
ISBN-10: 1009344676
Sprache: Englisch
Ausstattung / Beilage: HC gerader Rücken kaschiert
Einband: Gebunden
Autor: Kawamata, Yujiro
Hersteller: Cambridge University Press
Maße: 235 x 157 x 19 mm
Von/Mit: Yujiro Kawamata
Erscheinungsdatum: 22.05.2024
Gewicht: 0,537 kg
Artikel-ID: 128278093
Über den Autor
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).
Inhaltsverzeichnis
Preface; 1. Introduction; 2. Algebraic varieties with boundaries; 3. The minimal model program; 4. The finite generation theorem; Bibliography; Index.
Details
Erscheinungsjahr: 2024
Fachbereich: Allgemeines
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
ISBN-13: 9781009344678
ISBN-10: 1009344676
Sprache: Englisch
Ausstattung / Beilage: HC gerader Rücken kaschiert
Einband: Gebunden
Autor: Kawamata, Yujiro
Hersteller: Cambridge University Press
Maße: 235 x 157 x 19 mm
Von/Mit: Yujiro Kawamata
Erscheinungsdatum: 22.05.2024
Gewicht: 0,537 kg
Artikel-ID: 128278093
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