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In algebraic geometry, a relative effective Cartier divisor is roughly a family of effective Cartier divisors. Precisely, an effective Cartier divisor in a scheme X over a ring R is a closed subscheme D of X that is flat over R and the ideal sheaf I {\displaystyle I} of D is locally free of rank one. Equivalently, a closed subscheme D of X is an effective Cartier divisor if there is an open affine cover U i = Spec A i {\displaystyle U_{i}=\operatorname {Spec} A_{i}} of X and nonzerodivisors f i ∈ A i {\displaystyle f_{i}\in A_{i}} such that the intersection D ∩ U i {\displaystyle D\cap U_{i}} is given by the equation f i = 0 {\displaystyle f_{i}=0} and A / f i A {\displaystyle A/f_{i}A} is flat over R and such that they are compatible.
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