In algebraic geometry a normal crossing singularity is a singularity similar to a union of coordinate hyperplanes.
The term can be confusing because normal crossing singularities are not usually normal schemes (in the sense of the local rings being integrally closed).
Then Z is called a smooth normal crossing divisor if either Equivalently, one says that a reduced divisor has normal crossings if each point étale locally looks like the intersection of coordinate hyperplanes.
In algebraic geometry a normal crossings singularity is a point in an algebraic variety that is locally isomorphic to a normal crossings divisor.
In algebraic geometry a simple normal crossings singularity is a point in an algebraic variety, the latter having smooth irreducible components, that is locally isomorphic to a normal crossings divisor.