fibration of foliation XQ7KX6DA

fibration of foliation

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Theorem 1.3 (Main theorem). Let X be a projective Q-factorial toric variety and let F be a toric foliation of rank r on X. Then lF (R) := min [C]∈R{−KF · C} ≤ r + 1 holds for every extremal ray R of NE(X) = NE(X). Moreover, if lF (R) > r holds for some extremal ray R of NE(X), then the contraction morphism φR : X → Y associated to R is a Pr-bundle over Y . In this case, F = TX/Y holds, where TX/Y is the relative tangent sheaf of φR : X → Y . In particular, F is locally free. (pdf) (Fujino 和 Sato, 2024, p. 622)