Cox lc if X CY type MDS

Theorem 1.3. Let (X, ) be a projective Q-factorial log Calabi–Yau pair over C such that X is a Mori Dream Space, and let D1, … , Dr be a basis for the torsion free part of Cl(X). Then the ring Cox(X; D1, … , Dr ) is normal with log canonical singularities. (page) (Brown, 2013, p. 656)