Germ of an analytic set

Summary

The germ of an analytic set at a point $a$ records the shape of a complex analytic variety arbitrarily close to $a$. It forgets the rest of the set. Two analytic sets have the same germ at $a$ when they coincide on some neighbourhood of $a$. Germs of analytic sets at $a$ correspond to radical ideals of the ring of germs of holomorphic functions at $a$. This makes local analytic geometry a branch of commutative algebra.