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arXiv · 2303.10098

Mapping free resolutions of length three II -- Module formats

Sara Angela Filippini·Lorenzo Guerrieri
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Abstract

Let $M$ be a perfect module of projective dimension 3 in a Gorenstein, local or graded ring $R$. We denote by $\FF$ the minimal free resolution of $M$. Using the generic ring associated to the format of $\FF$ we define higher structure maps, according to the theory developed by Weyman in "Generic free resolutions and root systems" (Annales de l'Institut Fourier} 68.3 (2018), pp. 1241--1296). We introduce a generalization of classical linkage for $R$-module using the Buchsbaum--Rim complex, and study the behaviour of structure maps under this Buchsbaum--Rim linkage. In particular, for certain formats we obtain criteria for these $R$-modules to lie in the Buchsbaum--Rim linkage class of a Buchsbaum--Rim complex of length 3.

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Sara Angela Filippini, Lorenzo Guerrieri. 2023-03-17. Mapping free resolutions of length three II -- Module formats. https://arxiv.org/abs/2303.10098

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