Germ of a holomorphic function

Summary

A germ of a holomorphic function at a point $a \in \C^n$ is a holomorphic function defined near $a$. Two such functions are identified when they agree on some neighbourhood of $a$. It is the special case of a germ for holomorphic functions. The germs at $a$ form a ring $\mathcal{O}_{n,a}$, which is isomorphic to the ring of convergent power series in $n$ variables. Local analytic geometry studies this ring and its ideals.