Cox环的微分：Jaczewski定理的再认识
Differentials of Cox rings: Jaczewski's theorem revisited
摘要：
完备正规簇X上的广义欧拉序列是平凡丛V \otimes O_X通过微分微分层Ω_X的唯一扩张，通过包含线性空间V到Ext^1（O_X，Ω_X）中给出。对于Λ，一个Cartier因子格，令R_Λ表示由Λ中的第一类Chern因子类所张成的与V相关联的相应层。我们证明了任何投射的光滑簇，在其上丛R_Λ分裂成线丛的直和是环面的。我们用Cox环的特征空间上的微分微分层来描述丛R_Λ，只要它是双生成的.此外，我们还讨论了R_Λ的截模的有限性和Λ的Cox环的有限性。
英文摘要：
A generalized Euler sequence over a complete normal variety X is the unique extension of the trivial bundle V \otimes O_X by the sheaf of differentials Ω_X, given by the inclusion of a linear space V in Ext^1(O_X,Ω_X). For Λ, a lattice of Cartier divisors, let R_Λdenote 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 R_Λsplits into a direct sum of line bundles is toric. We describe the bundle R_Λin 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 R_Λand of the Cox ring of Λ.
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