Let $ X/k$ be a smooth projective variety over an algebraically closed field $ k$ . Q1: For any $ f \in k(X)$ , is there a prime divisor $ D_{\infty,f}$ and $ g \in k(X)$ such that $ fg$ has poles only at $ D_{\infty,f}$ , i.e. $ (fg)=\sum n_iD_i-mD_{\infty,f}$ for $ n_i,m>0$ ?Read more