Resolutions of modules with initially linear syzygies

Emil Sk\"oldberg

Resolutions of modules with initially linear syzygies

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arxiv 1106.1913 v2 pith:62HCNTGO submitted 2011-06-09 math.AC

Emil Sköldberg This is my paper · ORCID

classification math.AC

keywords linearresolutionsinitiallyminimalmodulessyzygiesadmitsclass

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We introduce the class of modules with initially linear syzygies, which includes ideals with linear quotients, and study their minimal resolutions. Using a contracting homotopy for the resolutions, we see that the minimal resolution of a matroidal monomial ideal admits a DGA structure.

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A family of simplicial resolutions which are DG-algebras
math.AC 2024-12 conditional novelty 7.0 of 10

Monomial ideals admit pivot resolutions that sit between Lyubeznik and Taylor resolutions, always carry a DG-algebra structure, and come with explicit Eisenbud-Shamash higher homotopies over complete intersections.

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