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Algebraic Varieties: Minimal Models and Finite Generation - Yujiro Kawamata Empty Algebraic Varieties: Minimal Models and Finite Generation - Yujiro Kawamata

Dom Jun 16, 2024 1:13 pm

Algebraic Varieties: Minimal Models and Finite Generation - Yujiro Kawamata 3087377e0e5eb35906b24b8ee0e4d793
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pdf | 8.65 MB | English | Isbn:9781009344678 | Author: Yujiro Kawamata, Chen Jiang (Translator) | Year: 2024
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About ebook: Algebraic Varieties: Minimal Models and Finite Generation

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.


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