Canonical divisor of a smooth variety
= Canonical divisor of a smooth variety
{title2=$\mathcal O_X(K_X)\cong\omega_X$}
A canonical divisor $K_X$ on a smooth integral variety is the <Cartier divisor> of a nonzero rational top-degree differential form; $\mathcal O_X(K_X)\cong\omega_X$. Its linear-equivalence class is independent of the chosen form. The <plurigenus> is the dimension of the space of sections of a positive tensor power of this bundle.