Umfang:
1 online resource (x, 251 pages)
,
digital, PDF file(s).
ISBN:
9781009344647
,
9781009344678
Serie:
Cambridge studies in advanced mathematics 214
Originaltitel:
Kōjigen daisū tayōtairon
Inhalt:
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.
Anmerkung:
Title from publisher's bibliographic system (viewed on 28 May 2024)
Weitere Ausg.:
ISBN 9781009344678
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe ISBN 9781009344678
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Kawamata, Yujiro, 1952 - Algebraic varieties Cambridge : Cambridge University Press, 2024 ISBN 9781009344678
Sprache:
Englisch
DOI:
10.1017/9781009344647
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