# ag.algebraic geometry – how to see the Gysin map explicitly in an easy situation

Let $$C$$ be a smooth projective curve and let $$U subset C$$ be an open affine subset, with closed complement $$S$$ consisting of a finite number of points. I am trying to see explicitly the Gysin map in algebraic de Rham cohomology
$$H^0_{dR}(S) longrightarrow H^2_{dR}(C).$$ By explicitly, I mean covering $$C$$ by $$U$$ and another affine open subset, say $$V$$, containing $$S$$ and computing $$H^2_{dR}(C)$$ a la Cech. In this way, every element can be represented by a global section of $$Omega^1$$ on $$U cap V$$. On the other hand, elements of $$H^0_{dR}(S)$$ are functions on $$S$$. So I am trying to find a way to produce a differential on $$U cap V$$ out of a function on $$S$$. I have the intuition that logarithmic derivative should play a role here but I am stuck. Can anyone help? Thanks!