Normal crossing divisor

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.


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