Toric divisor

Each ray $\rho$ of a fan determines a torus-invariant prime divisor $D_{\rho }$. Integer combinations of these divisors encode line bundles and maps from a toric variety.

For a character ${\chi }^m$ of the dense torus,

For a toric variety whose rays span $N_{\mathbb{R}}$, the divisor class group is computed bywhere $m\mapsto (⟨m,v_{\rho }⟩{)}_{\rho }$.

For an invariant divisor $D={\sum }_{\rho }{a}_{\rho }{D}_{\rho }$, its lattice polytope isIts lattice points index torus-character sections of the associated line bundle.

A divisor is basepoint-free when its global sections have no common zero. Its complete linear system therefore defines a Kodaira map everywhere.