toric for surface germ

6.4. Theorem. Let (SIZ, B) have a log canonical K + Band neflZ divisor -(K + B). Then p(SIZ) ~ I:bi - 2, where p(SIZ) is the rank of the Weil group modulo the algebraic equivalencelZ or just the Picard number when the singularities of S are rational. Moreover, the equality holds if and only if K + B == 0 and SIZ is formally toric with C = LBJ ~ D. In addition, in the case with the equality and reduced B = C, (SIZ, C) is formally toric with C = D (see Example 5.3). (page) (Shokurov, 2000, p. 3922)