Principal divisor on an algebraic curve
= Principal divisor on an algebraic curve
{title2=$(f)$}
= Principal divisor
{synonym}
For a nonzero <rational function> $f$ on a <smooth projective curve> $C$, its principal divisor is
$$
(f)=\operatorname{div}(f)=\sum_{p\in C}\operatorname{ord}_p(f)p.
$$
It records the zeros of $f$ with positive multiplicity and its poles with negative multiplicity. Every principal divisor has <degree of a divisor>[degree] zero.