Work

Mapping free resolutions of length three II - Module formats

Year: 2024

Type: article

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.

Source: Linear Algebra and its Applications

DOI: 10.1016/j.laa.2024.10.010

Authors: Sara Angela Filippini, Lorenzo Guerrieri

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,870

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Narodowe Centrum Nauki, Narodowa Agencja Wymiany Akademickiej, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni

Award: G7710824174