log canonical etc foliated toric DTXZ6RTA

log canonical etc foliated toric

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Proposition 0.4 (= Proposition 3.8). Let (FW , ∆) be a toric foliated pair on a Q-factorial toric variety XΣ. (1) (FW , ∆) is log canonical if and only if Supp(∆) ⊂ ⋃ ρ⊂W Dρ(= Supp(KFW )). (2) Suppose 0 < ε < 1. Then (FW , ∆) is ε-log canonical if and only if φ(KFW +∆)(u) ≥ ε for any primitive vector u ∈ |Σ| ∩ N such that R≥0u 6∈ Σ(1) where φ(KFW +∆) is the piecewise linear function associated with KFW + ∆. (3) FW is canonical if and only if for any σ ∈ Σ, the only non-zero elements of Πσ, W ∩ W ∩ N are contained in the facet of Πσ, W that does not contain the origin where Πσ, W is defined in Definition 3.6. (4) For any σ ∈ Σ, FW is terminal at the generic point of Vσ if and only if Πσ, W 6= σ and the elements of Πσ, W ∩ W ∩ N are vertices of Πσ, W . (pdf) (Chang 和 Chen, 2023, p. 2)