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Cellular resolutions of powers of monomial ideals

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arxiv 1212.2146 v3 pith:4DJ7LE4T submitted 2012-12-10 math.AC math.CO

Alexander Engstrom , Patrik Noren This is my paper · ORCID
classification math.ACmath.CO
keywords powersidealscellularcomplexesresolutionsedgeminimalpolyhedral
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There are many connections between the invariants of the different powers of an ideal. We investigate how to construct minimal resolutions for all powers at once using methods from algebraic and polyhedral topology with a focus on ideals arising from combinatorics. In one construction, we obtain cellular resolutions for all powers of edge ideals of bipartite graphs on n vertices, supported by (n-2)-dimensional complexes. Our main result is an explicit minimal cellular resolution for all powers of edge ideals of paths. These cell complexes are constructed by first subdividing polyhedral complexes and then modifying them using discrete Morse theory.

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  1. Morse resolutions of monomial ideals and Betti splittings

    math.AC 2025-02 conditional novelty 6.0 of 10

    Stable, vertex splittable, and linear quotient monomial ideals admit minimal pruned free resolutions, unifying the Eliahou-Kervaire and Herzog-Takayama constructions.

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