在他的论文“Religues of a Pfaff system relative to an invariant subscheme”（Trans.Amer.Math.Soc.352，2000，4019-4035）中，F. Sancho de Salas将环层$\mathcal{O}$上的模$M$的泛Koszul复形定义为${\rm Kos}(M)=Λ(M)\otimes_{\mathcal{O}}S(M)$，其中$Λ(M)$和$S(M)$代表$M$的外对称代数，赋予通常的微分，并证明了猜想（猜想2.3）。${\rm Kos}(M)$总是非循环的。本文给出了一个非循环Koszul复形${\rm Kos}(M)$的例子。
英文摘要：
In his paper "Residues of a Pfaff system relative to an invariant subscheme" in Trans. Amer. Math. Soc. 352, 2000, 4019-4035, F. Sancho de Salas defines the universal Koszul complex of a module $M$ over a sheaf of rings $\mathcal{O}$ as ${\rm Kos}(M)=Λ(M)\otimes_{\mathcal{O}}S(M)$, where $Λ(M)$ and $S(M)$ stand for the exterior and symmetric algebras of $M$, endowed with the usual differential, and he conjectures (Conjecture 2.3.) that ${\rm Kos}(M)$ is always acyclic. We give here an example of a non acyclic Koszul complex ${\rm Kos}(M)$.
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