Canonical divisor of the projective line ($K_{{\mathbb{P}}^1}$)

For the affine coordinate $t$ on ${\mathbb{P}}^1$, put $s=t^{-1}$ at infinity. Since $dt=-s^{-2}ds$,so $K_{{\mathbb{P}}^1}\sim -2\infty$. More generally,because $L(d\infty )$ consists of polynomials of degree at most $d$ when $d\ge 0$ and only the zero function when $d<0$.