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arXiv · 2412.21120

A family of simplicial resolutions which are DG-algebras

James Cameron·Trung Chau·Sarasij Maitra·Tim Tribone
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Abstract

Each monomial ideal over a polynomial ring admits a free resolution which has the structure of a DG-algebra, namely, the Taylor resolution. A pivot resolution of a monomial ideal, which we introduce, is a resolution that is always shorter than the Taylor resolution (unless the Taylor resolution is as short as possible) but still retains a DG-algebra structure. We study the basic properties of this family of resolutions including a characterization of when the construction is minimal. Following the work of Sobieska, we use the explicit nature of pivot resolutions to give formulae for the Eisenbud-Shamash construction of a free resolution of a given monomial ideal over complete intersections.

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James Cameron, Trung Chau, Sarasij Maitra, Tim Tribone. 2024-12-30. A family of simplicial resolutions which are DG-algebras. https://arxiv.org/abs/2412.21120

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