 Canonical divisor of a smooth variety

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.