Normal crossing divisor

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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 = Zi a reduced Cartier divisor, with Zi its irreducible components. Then Z is called a smooth normal crossing divisor if either

(i) A is a curve, or
(ii) all Zi are smooth, and for each component Zk, (Z-Z_k)|_{Z_k} is a smooth normal crossing divisor.