we translate some results for quasi-smooth intersection subvarieties to\n\nAcknowledgement. I thank Prof. Ugo Bruzzo and Tiago Fonseca for useful discus- sions. I also acknowledge support from FAPESP postdoctoral grant No. 2019/23499-7.\n\nLet M be a free abelian group of rank d , let N = Hom ( M, Z ) , and N R = N ⊗ Z R .\n\nif there exist k linearly independent primitive elements e\n\n, . . . , e k ∈ N such that σ = { µ\n\ne\n\n+ ⋯ + µ k e k } . • The generators e i are integral if for every i and any nonnegative rational number µ the product µe i is in N only if µ is an integer. • Given two rational simplicial cones σ , σ ′ one says that σ ′ is a face of σ ( σ ′ < σ ) if the set of integral generators of σ ′ is a subset of the set of integral generators of σ . • A ﬁnite set Σ = { σ\n\n, . . . , σ t } of rational simplicial cones is called a rational simplicial complete d -dimensional fan if:\n\nall faces of cones in Σ are in Σ ;\n\nif σ, σ ′ ∈ Σ then σ ∩ σ ′ < σ and σ ∩ σ ′ < σ ′ ;\n\nN R = σ\n\n∪ ⋅ ⋅ ⋅ ∪ σ t .\n\nA rational simplicial complete d -dimensional fan Σ deﬁnes a d -dimensional toric variety P d Σ having only orbifold singularities which we assume to be projective. Moreover, T ∶ = N ⊗ Z C
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