ABSTRACT
For the local theory it is really sufficient merely to consider germs of holomorphic subvarieties at a single point in Cn—say, the origin. After having established some algebraic properties of the local rings of holomorphic functions, this chapter explores what might be considered the geometric properties of these local rings. It is concerned with the local properties of holomorphic subvarieties. In general, germs (equivalence classes) of holomorphic subvarieties will be denoted by boldface letters. In the general discussion of germs of holomorphic subvarieties it is probably less confusing to ignore equivalence relation most of the time, letting it remain understood though that these equivalence classes are the basic entities of interest here.
