toric projective bundles 3L8HHICB

toric projective bundles

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Lemma 6.1 (Toric projective bundles, [O1, p.41 Remark]). Let φ : X → Y be a toric morphism of toric varieties such that φ : X → Y is a Pr-bundle. Then X ≃ PY (L0 ⊕ · · · ⊕ Lr) for some line bundles L0, . . . , Lr on Y and φ : X → Y is isomorphic to the projection π : PY (L0 ⊕ · · · ⊕ Lr) → Y . (pdf) (Fujino 和 Sato, 2024, p. 10)