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Given a zero-dimensional Gorenstein algebra $\mathbb{B}$ and two syzygiesbetween two elements $f_1,f_2\in\mathbb{B}$, one constructs a double complex of$\mathbb{B}$-modules, ${\cal G}_\mathbb{B},$ called the small Gobelin. Wedescribe an inductive procedure to construct the even and odd hyperhomologiesof this complex. For high degrees, the difference $\dim \mathbb{H}_{j+2}({\calG}_\mathbb{B}) - \dim\mathbb{H}_j({\cal G}_\mathbb{B})$ is constant, butpossibly with a different value for even and odd degrees. We describe two flagsof ideals in $\mathbb{B}$ which codify the above differences of dimension. Themotivation to study this double complex comes from understanding the tangencycondition between a vector field and a complete intersection, and invariantsconstructed in the zero locus of the vector field $\hbox{Spec}(\mathbb{B})$.

On the Hyperhomology of the Small Gobelin in Codimension 2