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lojasiewicz s introduction complex analytic geometry 1991

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Textbook in PDF format Preface to the Polish Edition Preface to the English Edition Preliminarios: algebra Rings, fields, modules, ideals, vector spaces Polynomials Polynomial mappings Symmetric polynomials. Discriminant Extensions of fields Factorial rings Primitive element theorem Extensions of rings Noetherian rings Local rings Localization Krull's dimension Modules of syzygies and homological dimension The depth of a module Regular rings Topology Some topological properties of sets and families of sets Open, closed and proper rnappings Local homeomorphisms and coverings Germs of sets and functions The topology of a finite dimension al vector space (over C or R) The topology of the Grassmann space Complex analysis Holomorphic mappings The Weierstrass preparation theorem Complex manifolds The rank theorem. Submersions Rings of germs of holomorphic functions Elementary properties. Noether and local properties. Regularity Unique factorization property The Preparation Theorem in Thom-Martinet version Analytic sets, analytic germs and their ideals Dimension Thin sets Analytic sets and germs Ideals of germs and the loci of ideals. Decomposition into simple germs Principal germs One-dimensional germs. The Puiseux theorem Fundamental lemmas Lemmas on quasi-covers Regular and k-normal ideals and germs Rückert's descriptive lemma Hilbert's Nullstellensatz and other consequences (concerning dimension, regularity and k-normality) Geometry of analytic sets Normal triples Regular and singular points. Decomposition into simple components Some properties of analytic germs and sets The ring of an analytic germ. Zariski's dimension The maximum principle The Remmert-Stein removable singularity theorem Regular separation Analytically constructible sets Holomorphic mappings Some properties of holomorphic mappings of manifolds The multiplicity theorem. Rouché's theorem Holomorphic mappings of analytic sets Analytic spaces Remmert's proper mapping theorem Remmert's open mapping theorem Finite holomorphic mappings c-holomorphic mappings Normalization The Cartan and Oka coherence theorems Normal spaces. Universal denominators Normal points of analytic spaces Normalization Analyticity and algebraicity Algebraic sets and their ideals The projective space as a manifold The projective closure of a vector space Grassmann manifolds Blowings-up Algebraic sets in projective spaces. Chow's theorem The Rudin and Sadullaev theorems Constructible sets. The Chevalley theorem Rückert's lemma for algebraic sets Hilbert's Nullstellensatz for polynomials Further properties of algebraic sets. Principal varieties. Degree The ring of an algebraic subset of a vedor space Bézout's theorem. Biholomorphic mappings of projective spaces Meromorphic functions and rational functions Ideals of O_n with polynomial generators Serre's algebraic graph theorem Algebraic spaces Biholomorphic mappings of factorial subsets in projective spaces The Andreotti-Salmon theorem Chow's theorem on biholomorphic mappings of Grassmann manifolds References Notation index Subject index

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lojasiewicz s introduction complex analytic geometry 1991