书籍 Algebraic Geometry 作者：Lunifans 发布于 2026-06-30T15:00:59Z · 公开内容更新于 2026-06-30T07:00:59Z Prerequisites 书籍信息 作者J.S. Milne 作者实体J.S. Milne 目录Introduction1 Preliminaries from commutative algebraa Rings and idealsb Rings of fractionsc Unique factorizationd Integral dependencee Tensor Productsf Transcendence basesExercises2 Algebraic Setsa Definition of an algebraic setb The Hilbert basis theoremc The Zariski topologyd The Hilbert Nullstellensatze The correspondence between algebraic sets and radical idealsf Finding the radical of an idealg Properties of the Zariski topologyh Decomposition of an algebraic set into irreducible algebraic setsi Regular functions; the coordinate ring of an algebraic setj Regular mapsk Hypersurfaces; finite and quasi-finite mapsl Noether normalization theoremm DimensionExercises3 Affine Algebraic Varietiesa Sheavesb Ringed spacesc The ringed space structure on an algebraic setd Morphisms of ringed spacese Affine algebraic varietiesf The category of affine algebraic varietiesg Explicit description of morphisms of affine varietiesh Subvarietiesi Properties of the regular map Spm(a)j Affine space without coordinatesk Birational equivalencel DimensionExercises4 Local Studya Tangent spaces to plane curves 进入阅读 相关 Tagalgebraic-geometry代数几何