facts. An elementary acquaintance with topology, algebra, and analysis (inยญ cluding the notion of a manifold) is sufficient as far as the understanding of this book is concerned. All the necessary properties and theorems have been gathered in the preliminary chapters -either with proofs or with references to standard and elementary textbooks. The first chapter of the book is devoted to a study of the rings Oa of holomorphic functions. The notions of analytic sets and germs are introduced in the second chapter. Its aim is to present elementary properties of these objects, also in connection with ideals of the rings Oa. The case of principal germs (ยง5) and one-dimensional germs (Puiseux theorem, ยง6) are treated separately. The main step towards understanding of the local structure of analytic sets is Ruckert's descriptive lemma proved in Chapter III. Among its conseยญ quences is the important Hilbert Nullstellensatz (ยง4). In the fourth chapter, a study of local structure (normal triples, ยง 1) is followed by an exposition of the basic properties of analytic sets. The latter includes theorems on the set of singular points, irreducibility, and decomยญ position into irreducible branches (ยง2). The role played by the ring 0 A of an analytic germ is shown (ยง4). Then, the Remmert-Stein theorem on reยญ movable singularities is proved (ยง6). The last part of the chapter deals with analytically constructible sets (ยง7)
CONTENT
A. Algebra -- B. Topology -- C. Complex analysis -- I. Rings of germs of holomorphic functions -- II. Analytic sets, analytic germs and their ideals -- III. Fundamental lemmas -- IV. Geometry of analytic sets -- V. Holomorphic mappings -- VI. Normalization -- VII. Analyticity and algebraicity -- References -- Notation index
