ABSTRACT
The analysis of holomorphic varieties can be used to complete in some points the discussion of holomorphic extensions of holomorphic functions. This chapter considers the results about holomorphic extensions of functions in subsets of Cn, since a corresponding analysis of extension of holomorphic functions on arbitrary holomorphic varieties leads to rather different phenomena that will be treated later. It describes the sort of extension theorem which can be rephrased as the assertion that any function holomorphic in the complement of a holomorphic submanifold V of codimension at least two in an open subset D?Cn can always be extended uniquely to a holomorphic function in all of D. For holomorphic subvarieties there are extension theorems that are quite analogous to the preceding extension theorems for holomorphic functions. The chapter discusses two lemmas to begin the discussion of these extension theorems.
