Higher-Dimensional Algebraic Geometry
Higher-Dimensional Algebraic Geometry
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DOI：
10.1007/978-1-4757-5406-3
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
O. Debarre
中科院分区：
文献类型：
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作者：
O. Debarre
高维代数几何研究代数簇的分类理论。这一非常活跃的研究领域仍在发展中，但在过去的二十年里积累了数量惊人的知识。作者的目标是为这一主题提供一个容易理解的介绍。该书在开始时涵盖了预备和标准定义和结果，接着讨论了具有许多有理曲线的光滑射影簇几何的各个方面，最后通过证明锥形和压缩定理，向Mori的代数簇分类的最小模型程序迈出了第一步。
Higher-Dimensional Algebraic Geometry studies the classification theory of algebraic varieties. This very active area of research is still developing, but an amazing quantity of knowledge has accumulated over the past twenty years. The author's goal is to provide an easily accessible introduction to the subject.The book covers in the beginning preparatory and standard definitions and results, moves on to discuss various aspects of the geometry of smooth projective varieties with many rational curves, and finishes in taking the first steps towards Mori's minimal model program of classification of algebraic varieties by proving the cone and contraction theorems.