= Degree of a line bundle
{title2=$\deg L=\deg D\quad\text{when }L\cong\mathcal O_C(D)$}
On a smooth projective curve, a nonzero <rational section> represents a <line bundle> by its <divisor on an algebraic curve>. The degree is the sum of its vanishing orders minus its pole orders, including residue-field degrees over a nonclosed field. Principal <divisors on an algebraic curve> have degree zero, so this number is independent of the section. A nonzero regular section gives an <effective divisor> and therefore a nonnegative degree. Degrees add under tensor products and change sign under duality.
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