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arXiv · 2403.18507

CI-sequences and almost complete intersections

Giuseppe Zappalà
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Abstract

We study the Hilbert function and the graded Betti numbers of almost complete intersection artinian algebras. We show that that every Hilbert function of a complete intersection artinian algebra is the Hilbert function of an almost complete intersection algebra. In codimension $3$ we focus on almost complete intersection artinian algebras whose Hilbert function coincides with that of a complete intersection defined by $3$ forms of the same degree. We classify all the possible graded Betti numbers of such algebras and we specify what cancellations are allowed in a minimal graded free resolution.

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Giuseppe Zappalà. 2024-03-27. CI-sequences and almost complete intersections. https://arxiv.org/abs/2403.18507

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