ABSTRACT

One common application of Remmer's proper mapping theorem is the observation that the image of a compact holomorphic variety V under any holomorphic mapping F:V ? W is a holomorphic subvariety of W, since any continuous mapping from a compact Hausdorff space to another topological space is necessarily proper. It may be worth noting in passing that not every semiproper mapping is necessarily closed. The monoidal transform is a special case of an important general class of holomorphic mappings, and the consideration of this special case in detail first may have served to motivate and make more intuitively clear the brief discussion of the general class. The theory of resolution of singularities is an extensive field in itself, and some acquaintance with holomorphic modifications is useful to anyone interested in complex analysis. The chapter considers a common construction of holomorphic modifications.