Basepoint-free divisor

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

For an invariant Cartier divisor $D={\sum }_{\rho }{a}_{\rho }{D}_{\rho }$ on a complete smooth toric variety, let $m_{\sigma }$ satisfy $⟨m_{\sigma },v_{\rho }⟩=-a_{\rho }$ for rays in a maximal cone $\sigma$. The divisor is basepoint-free exactly when every $m_{\sigma }$ lies in the lattice polytope of a toric divisor $P_D$. Its character section then trivializes the line bundle on the entire chart $U_{\sigma }$.

// Target: geometry-and-topology.bigb