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Higher structure maps for free resolutions of length 3 and linkage

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arxiv 2208.05934 v3 pith:HB3Q3Y7E submitted 2022-08-11 math.AC

Lorenzo Guerrieri , Xianglong Ni , Jerzy Weyman This is my paper · ORCID
classification math.AC
keywords freeidealmapsmathbbresolutionlicciperfectring
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abstract

Let $I$ be a perfect ideal of height 3 in a Gorenstein local ring $R$. Let $\mathbb{F}$ be the minimal free resolution of $I$. A sequence of linear maps, which generalize the multiplicative structure of $\mathbb{F}$, can be defined using the generic ring associated to the format of $\mathbb{F}$. Let $J$ be an ideal linked to $I$. We provide formulas to compute some of these maps for the free resolution of $J$ in terms of those of the free resolution of $I$. We apply our results to describe classes of licci ideals, showing that a perfect ideal with Betti numbers $(1,5,6,2)$ is licci if and only if at least one of these maps is nonzero modulo the maximal ideal of $R$.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The linkage class of a grade three complete intersection

    math.AC 2024-11 conditional novelty 7.0 of 10

    Grade three licci ideals are classified up to deformation by Weyl group double coset data, with explicit minimal free resolutions for each class.

  2. Generic models of licci ideals parametrized by Schur functors

    math.AC 2025-06 conditional novelty 6.0 of 10

    Herzog classes of codimension-3 licci ideals are parametrized by pairs of partitions via a graph of direct links, with applications to Tor algebra structures.

  3. Residual Intersections and Schubert Varieties

    math.AG 2024-11 conditional novelty 6.0 of 10

    For ADE types with an extremal or minuscule vertex, each opposite Schubert variety on one arm of the graph G_k has defining ideal given by a residual intersection of the linked variety on the other arm.

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