Complex Analytic Sets

The Theory of holomorphic functions of several complex variables is undergoing rapid developments. An important aspect of this developmnet is the study of zero sets of functions which are of great importance in algebraic and differential geometry and related areas. This is the first book to be published in which zero sets of holomorphic functions of several complex variables are studied from a geometric point of view.

The material is presented in a way that leads the reader from more established material e.g. Whitney cones,through to more revent  material. e.g. currents, and thence to the frontier of current research in this field.

Other topics covered include: local structure,decomposition, tangent cones, singularities, metric theory(in particular,growth theory in the spirit of R, Nevanlinna),boundary behaviour, and continuation. Many results from chapters 3-4 are new. Furthermore,six appendices make the book self-contained.