I am currently studying algebraic curves using the Fulton. In chapter 8 we have a proposition called "Residue Theorem"
RESIDUE THEOREM. Let $C,E$ be as above ($C$ is a projective plane curve, $E = \sum_{Q\in X} (m_{(f(Q)} - 1)\, Q$, $X$ is a non singular model of $C$). Suppose $D$ and $D'$ are effective divisors on $X$, with $D'\equiv D$. Suppose $G$ is an adjoint of degree $m$ such that $\operatorname{div}(G) = D + E + A$ for some effective divisor $A$. Then there is an adjoint $G'$ of degree $m$ such that $\operatorname{div}(G') = D' + E + A$.
I was wondering if this has anything to do with the Residue Theorem in complex analysis. Can anyone help me?