| 代数几何是近代以来发展迅速的一门数学的分支学科，与其他领域的许多学科有着紧密的联系，也是高等院校数学专业研究生阶段所开设的一门非常重要的基础课程。 本书是时下为数不多的代数几何的经典教材之一，已被众多学校用做教学参考书。与本书相配套的教材《The Red Book of Varieties and Schemes》和《Algebraic Geometry GTM52》也已影印出版。本书是由作者多年来在各处讲授代数几何课的笔记，经多次修订后整理成册。全书的前一部分主要介绍了复射影簇，后一部分则重点探讨了概型，内容包括概型的凝聚层的上同调与应用。 |
Introduction Prerequisites Chapter 1. Affine Varieties 1A. Their Definition, Tangent Space, Dimension, Smooth and Singular Points. 1B. Analytic Uniformization at Smooth Points, Examples of Topological Knottedness at Singular Points 1C. Ox,xa UFD when x Smooth; Divisor of Zeroes and Poles of Functions Chapter 2. Projective Varieties 2A. Their Definition, Extension of Concepts from Aftine to Projective Case 2B. Products, Segre Embedding, Correspondences 2C. Elimination Theory, Noether's Normalization Lemma, Density of Zariski-Open Sets Chapter 3. Structure of Correspondences 3A. Local Properties——Smooth Maps, Fundamental Openness Principle, Zariski's Main Theorem 3B. Global Propcrties——Zariski's Connectedness Theorem, Specialization Principle 3C. Intersections on Smooth Varieties Chapter 4. Chow's Theorem 4A. Internally and Externally Defined Analytic Sets and their Local Descriptions as Branched Coverings of C'. 4B. Applications to Uniqueness of Algebraic Structure and |
内容加载中，请稍后...
商品评论（0条）