Books 2 and 3 correspond to Chap. V-IX of the first edition. They study schemes and complex manifolds, two notions that generalise in different directions the varieties in projective space studied in Book 1. Introducing them leads also to new results in the theory of projective varieties. For example, it is within the framework of the theory of schemes and abstract varieties that we find the natural proof of the adjunction formula for the genus of a curve, which we have already stated and applied in Chap. IV, 2.3. The theory of complex analytic manifolds leads to the study of the topology of projective varieties over the field of complex numbers. For some questions it is only here that the natural and historical logic of the subject can be reasserted; for example, differential forms were constructed in order to be integrated, a process which only makes sense for varieties over the (mai or) complex fields. Changes from the First Edition
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域扩张和拓扑上流形是代数几何中仿射簇推广的两个方向；O（specA)=A;向量丛仅仅是集合论，而局部自由层则是代数结构；环的谱同构于谱的闭子集。代数闭域中代数簇X，正规函数环K（X)；对应任意环A谱spec（A),和结构环层O，结构层的茎不依赖它是不是点还是邻域
评分适合浅尝辄止
评分入门书，但是没看过后半部分，前半部分不错。
评分域扩张和拓扑上流形是代数几何中仿射簇推广的两个方向；O（specA)=A;向量丛仅仅是集合论，而局部自由层则是代数结构；环的谱同构于谱的闭子集。代数闭域中代数簇X，正规函数环K（X)；对应任意环A谱spec（A),和结构环层O，结构层的茎不依赖它是不是点还是邻域
评分适合浅尝辄止
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