= Degree-zero Picard group of a curve
{title2=$\operatorname{Pic}^0(C)$}
= Degree-zero Picard groups of a curve
{synonym}
For a <smooth projective curve>, the degree-zero Picard group consists of <line bundles> of degree zero up to isomorphism, with tensor product as addition. A nonzero <rational section of a line bundle> identifies each <line bundle> with $\mathcal O(D)$ for a <divisor on an algebraic curve>; degree is the sum of multiplicities weighted by residue-field degrees. Over an <algebraically closed field>, every degree-zero <divisor> is a sum of differences of points.
Back to article page
