Divisor on a complex manifold
= Divisor on a complex manifold
A divisor on a <complex manifold> is a locally finite formal sum
$$
D=\sum_Yn_YY,
$$
where the $Y$ are irreducible complex analytic hypersurfaces and $n_Y\in\mathbb Z$. Products of powers of <local defining function of a complex analytic hypersurface>[local defining functions] give local meromorphic equations $f_\alpha$ for $D$ whose ratios $f_\alpha/f_\beta$ are nowhere-vanishing holomorphic functions.