formally toric

Theorem 1. Let (X/Z, B) be a log canonical pair over a normal variety Z and let z ∈ Z be a closed point. Assume that −(KX + B) is nef over a neighborhood of z ∈ Z. Then, cz(X/Z, B) ≥ 0. Furthermore, if equality holds, then the following conditions are satisfied: 1. KX + B ∼Q,Z 0; 2. X → Z is formally toric at z; and, 3.. under the formal isomorphism of (2), the components of ⌊B⌋ are mapped to the completion of torus invariant divisors. (page) (Moraga and Svaldi, 2025, p. 2)