Effective Cartier divisor
= Effective Cartier divisor
= Effective divisor
{synonym}
An effective Cartier divisor is cut out locally by one <non-zero-divisor>; it is a codimension-one closed subscheme. On an integral scheme a nonzero <global section> of a <line bundle> defines such a divisor, possibly empty. On a nonreduced scheme a nonzero section need not be regular, so its zero locus need not be a Cartier divisor.