r=1 case

LEMMA 3.3 Let X be a Q-factorial Kawamata log terminal projective variety of dimension n, and let .X; / be a log canonical pair. Let D D P ai Si be a decomposition of . If (1) KX C is numerically trivial, (2) d D Pk iD1 ai > n, and (3) S1; S2; : : : ; Sk all span the same ray of the cone of effective divisors, then the Picard number of X is 1.

(page) (Brown et al., 2018, p. 948)