Toric basepoint-free criterion
= Toric basepoint-free criterion
For an invariant Cartier divisor $D=\sum_\rho a_\rho D_\rho$ on a complete smooth toric variety, let $m_\sigma$ satisfy $\langle m_\sigma,v_\rho\rangle=-a_\rho$ 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