Normal crossing divisor

In algebraic geometry, normal crossing divisors are a class of divisors which generalize the smooth divisors. Intuitively they cross only in a transversal way.

Let "A" be an algebraic variety, and $Z=\; Z\_i$ a reduced Cartier divisor, with $Z\_i$ its irreducible components. Then "Z" is called a smooth normal crossing divisor if either

:(i) "A" is a curve, or :(ii) all $Z\_i$ are smooth, and for each component $Z\_k$, $(Z-Z\_k)|\_\{Z\_k\}$ is a smooth normal crossing divisor.