抄録
A generalized Euler sequence over a complete normal variety X is the unique extension of the trivial bundle V ⊗ \mathcal{O}X by the sheaf of differentials ΩX, given by the inclusion of a linear space V ⊂ Ext1X(\mathcal{O}X, ΩX). For Λ, a lattice of Cartier divisors, let ℛΛ denote the corresponding sheaf associated to V spanned by the first Chern classes of divisors in Λ. We prove that any projective, smooth variety on which the bundle ℛΛ splits into a direct sum of line bundles is toric. We describe the bundle ℛΛ in terms of the sheaf of differentials on the characteristic space of the Cox ring, provided it is finitely generated. Moreover, we relate the finiteness of the module of sections of ℛΛ and of the Cox ring of Λ.
