A simple normal crossing divisor on a smooth variety is a divisor whose distinct irreducible components are smooth and meet transversely. In local regular coordinates its reduced support has equation
 |
where 
is at most the dimension of the variety. The same definition
uses local holomorphic coordinates on a complex manifold.
For example, the two coordinate axes in 
have simple normal crossings. A single irreducible nodal
curve does not, because its component is singular.
A rational boundary with simple normal crossing support may assign different rational coefficients to the components. For logarithmic Kodaira dimension, the compactification boundary is instead reduced, so every component has coefficient one.
