has foliated log resulution FCNB9GR4

has foliated log resulution

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Lemma 6.2.4. Let X be a normal quasi-projective variety, B an R-divisor on X, M a nef/X b-divisor on X, and F a foliation on X that is induced by a dominant map f : X 99K Z. Then: (1) If f is a contraction, then for any equi-dimensional model f ′ : (X′, ΣX′ , M) → (Z′, ΣZ′) of f : (X, B, M) → Z associated with h : X′ → X and hZ : Z′ → Z, h is a foliated log resolution of (X, F, B, M) and h−1F is induced by f ′. (2) (X, F, B, M) has a foliated log resolution. (pdf) (Chen 等, 2023, p. 45)