On a transform of an acyclic complex of length 3
Kosuke Fukumuro, Taro Inagawa, Koji Nishida
TL;DR
This paper presents a method to transform a length-3 acyclic complex resolving an ideal into another that resolves its colon with a parameter ideal, with applications to symbolic powers of minors.
Contribution
It introduces a concrete procedure to modify acyclic complexes of length 3 to resolve colon ideals, expanding tools for ideal resolutions.
Findings
Explicit procedure for transforming acyclic complexes
Application to computing symbolic powers of minors
Enhanced understanding of ideal resolutions in Cohen-Macaulay rings
Abstract
Let (R, m) be a Cohen-Macaulay local ring and Q a parameter ideal of R. Suppose that an acyclic complex of length 3 which is an R-free resolution of an ideal I of R is given. In this paper, we describe a concrete procedure to get an acyclic complex of length 3 that becomes an R-free resolution of I : Q. As an application, we compute the symbolic powers of ideals generated by maximal minors of certain 2 x 3 matrices.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic structures and combinatorial models