Logarithmic Enriques surfaces
De‐Qi Zhang · Kyoto journal of mathematics · 1991
3 ) Suppose that NKR is a Cartier divisor.Then E :=4*(NKv)-NK v is a Cartier divisor an d supported by SuppD.B y the assertion (2), we see E-ND*' --0.Since SuppD 5 USuppE is contained in SuppD w hich has negative intersection matrix, we must have NE 5 = E .Hence N D* is an integral divisor and f*(NKR)=N (D 5 +1( v ).Suppose that N D* is an integral divisor.Since (N(PL-which is a Cartier divisor.Hence N K r: is a Cartier divisor.Q. E. D