fano type is MDS

LEMMA 2.5.3 Let X be a normal projective variety. The following are equivalent. (1) We may find a Kawamata log terminal pair .X; / such that .KX C / is ample. (2) We may find a Kawamata log terminal pair .X; / such that .KX C / is big and nef. (3) We may find a Kawamata log terminal pair .X; / such that KX C is numerically trivial and is big. In particular, if X is Q-factorial, then X is a Mori dream space. paper Brown et al., 2018, p. 946