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首页> 外文期刊>Sugaku expositions: A translation of Sugaku >RECENT DEVELOPMENTS IN MINIMAL MODEL THEORY
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RECENT DEVELOPMENTS IN MINIMAL MODEL THEORY

机译：最小模型理论的最新发展

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摘要

The birational classification of algebraic varieties is a central problem in algebraic geometry. Starting with Riemann's theory of curves in the 19th century and the Italian school's theory of surfaces at the turn of the 20th century, passing through Kodaira's classification of complex analytic surfaces and the work of the Russian school under Shafarevich, a rather satisfactory classification was obtained for al-gebraic varieties in low dimensions. The first systematic attempt at a birational classification of algebraic varieties in dimension three and above was due to Iitaka [I1]; from the 1970s onwards, he introduced the notion of the Kodaira dimension of a general algebraic variety, thus taking the first step in the direction of birational classification. Iitaka's many contributions to the subject include the definition of log Kodaira dimension and his additivity conjecture for Kodaira dimension [I2]. These ideas can all be summarized as the Iitaka program.
机译：代数变种的二元分类是代数几何中的一个中心问题。从19世纪Riemann的曲线理论和20世纪初的意大利学派的曲面理论开始，通过Kodaira对复杂解析面的分类以及Shafarevich领导下的俄罗斯学派的工作，获得了相当令人满意的分类。低维的代数变体。 Iitaka [I1]首次对三维及以上维数的代数变分进行双分类。从1970年代起，他引入了一般代数变体的Kodaira维数的概念，从而朝双分分类法迈出了第一步。 Iitaka对这个问题的许多贡献包括对数Kodaira维的定义和他对Kodaira维的加和猜想[I2]。这些想法可以概括为Iitaka程序。

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