[citation needed] A unibranch local ring is said to be geometrically unibranch if the residue field of B is a purely inseparable extension of the residue field of Ared.
A complex variety X is called topologically unibranch at a point x if for all complements Y of closed algebraic subsets of X there is a fundamental system of neighborhoods (in the classical topology) of x whose intersection with Y is connected.
For example, there is the following result: Theorem [1] Let X and Y be two integral locally noetherian schemes and
In particular, if f is birational, then the fibers of unibranch points are connected.
You can help Wikipedia by expanding it.This commutative algebra-related article is a stub.