local generators of toric foliation STKZH45F

local generators of toric foliation

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Lemma 1.7 ([Pan15, Lemma 2.1.12]). Let W be an r-dimensional complex vector subspace of NC and let Σ be a fan in NR. For any ray ρ ∈ Σ(1) with the primitive generator vρ, if ρ ⊂ W , then we choose v2, . . . , vn so that {vρ, v2, . . . , vr} forms a basis for W . Otherwise, we just choose {v1, . . . , vr} to be a basis for W . Then FW |Uρ is generated by δv1 , . . . , δvr if ρ 6⊂ W 1 χmρ δvρ, δv2 , . . . , δvr if ρ ⊂ W . (pdf) (Chang 和 Chen, 2023, p. 5)