About: Formal holomorphic function

In algebraic geometry, a formal holomorphic function along a subvariety V of an algebraic variety W is an algebraic analog of a holomorphic function defined in a neighborhood of V. They are sometimes just called holomorphic functions when no confusion can arise. They were introduced by Oscar Zariski . The theory of formal holomorphic functions has largely been replaced by the theory of formal schemes which generalizes it: a formal holomorphic function on a variety is essentially just a section of the structure sheaf of a related formal scheme.