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arXiv · 2611.08764

Pruning free resolutions over a complete intersection

Ben Betts·Janet Vassilev
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Abstract

Given a free resolution $F_\bullet$ over a polynomial ring $R$ and a system of higher homotopies on it for a regular sequence $a_1,\dots,a_c$, we can use the Eisenbud-Shamash construction to build a free resolution over $\overline{R}=R/(a_1,\dots,a_c)$. We provide a combinatorial formula for the new system of higher homotopies on a pruned free resolution $F_{\bullet}^{\mathcal{M}}$ that corresponds to a pruning of the Eisenbud-Shamash resolution.

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Ben Betts, Janet Vassilev. 2026-11-05. Pruning free resolutions over a complete intersection. https://arxiv.org/abs/2611.08764

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