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Auteurs principaux: Guerrieri, Lorenzo, Ni, Xianglong, Weyman, Jerzy
Format: Preprint
Publié: 2025
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Accès en ligne:https://arxiv.org/abs/2506.09598
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author Guerrieri, Lorenzo
Ni, Xianglong
Weyman, Jerzy
author_facet Guerrieri, Lorenzo
Ni, Xianglong
Weyman, Jerzy
contents Let R be a commutative Noetherian ring. Licci ideals are the ideals of R that can be linked in a finite number of steps to a complete intersection. Each licci ideal admits a rigid deformation, and two licci ideals are in the same Herzog class if they have a common deformation. In this work, we show how all the Herzog classes of licci ideals of codimension 3 can be parametrized in terms of pairs of partitions associated to Schur functors. This fact allows to describe in a purely combinatorial way the (infinite) graph whose vertices correspond to Herzog classes and edges represent direct links between representatives of such classes. As applications, we obtain results on the classification of multiplications in Tor Algebras, and new structure theorems for families of licci ideals. In the final section, we extend many of these results to arbitrary codimension, but under some conjectural assumptions.
format Preprint
id arxiv_https___arxiv_org_abs_2506_09598
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Generic models of licci ideals parametrized by Schur functors
Guerrieri, Lorenzo
Ni, Xianglong
Weyman, Jerzy
Commutative Algebra
13D02, 13C05, 13C40
Let R be a commutative Noetherian ring. Licci ideals are the ideals of R that can be linked in a finite number of steps to a complete intersection. Each licci ideal admits a rigid deformation, and two licci ideals are in the same Herzog class if they have a common deformation. In this work, we show how all the Herzog classes of licci ideals of codimension 3 can be parametrized in terms of pairs of partitions associated to Schur functors. This fact allows to describe in a purely combinatorial way the (infinite) graph whose vertices correspond to Herzog classes and edges represent direct links between representatives of such classes. As applications, we obtain results on the classification of multiplications in Tor Algebras, and new structure theorems for families of licci ideals. In the final section, we extend many of these results to arbitrary codimension, but under some conjectural assumptions.
title Generic models of licci ideals parametrized by Schur functors
topic Commutative Algebra
13D02, 13C05, 13C40
url https://arxiv.org/abs/2506.09598