= Picard group of the projective line
{c}
{title2=$\operatorname{Pic}(\mathbf P^1_k)\cong\mathbb Z$}
For any <field> $k$, degree identifies the <Picard group> of the <projective line> with $\mathbb Z$, generated by $\mathcal O(1)$. A closed point on the affine chart is cut out by an irreducible polynomial $f(t)$, whose <divisor> is that point minus $\deg(f)$ times infinity. Hence every divisor is linearly equivalent to its degree times infinity. Principal divisors have degree zero, so the degree map is injective as well as surjective. Thus a <line bundle> of degree $d$ is $\mathcal O(d)$.
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