I need to find divisor of function:
$f(w_0,w_1,w_2)=(w_{0}^{2},w_1w_2)$
on $S=\left \{ w_0w_1-w_2w_3=0 \right \}\subseteq P^3$. And the question is do I need to take into account this surface? There is my solution:
Firstly we will find zeros and poles of f:
$f=0: D=\left \{ w_0=0 \right \}.$
$f= \infty :$ $L_1= \left \{w_1=0 \right \} ; L_2=\left \{ w_2=0 \right \} $
$(f)=mD-n_1L_1-n_2L_2$
Let us take Affine set $A=\left \{ w_3\neq 0 \right \}$ where $x=\frac{w_0}{w_3}, y=\frac{w_1}{w_3}, z=\frac{w_2}{w_3}$. After the intersection of A with 3 curves, we get:
$A\cap D=\left \{ x=0 \right \}; A\cap L_1=\left \{ y=0 \right \};A\cap L_2=\left \{ z=0 \right \}$
hence: $f(x,y,z)=\frac{x^2}{yz}$, so $m=2, n_1=n_2=1$, and $(f)=2D-L_1-L_2$
Is it right? Thanks!