For any effective divisor $D=\sum a_i[Y_i]$, in the language of complex spaces, $\mathcal{O}_D$ is the structure sheaf of the (possibly non-reduced) subspace associated to $D$.
I wonder what the subspace associated to $D$ is? I only know we can associate a line bundle for a divisor, $L(D)\to M$. Is $\mathcal{O}_D$ related to the sheaf $L(D)$, which is the sheaf of sections of the line bundle $L(D)\to M$.