Linear quotients, linear resolutions and the lcm-lattice

Fuente: arXiv
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Autor principal: Varshavsky, Roni
Formato: Preprint
Publicado: 2025
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author Varshavsky, Roni
author_facet Varshavsky, Roni
contents Linear resolutions and the stronger notion of linear quotients are important properties of monomial ideals. In this paper, we fully characterize linear quotients in terms of the lcm-lattice of monomial ideals. We also formulate an analogous characterization for monomial ideals with linear resolutions, making explicit a relationship that is implicit in the existing literature. These results complement characterizations of these two properties in terms of the Alexander dual of the corresponding Stanley-Reisner simplicial complex. In addition, we discuss applications to the case of edge ideals.
format Preprint
id arxiv_https___arxiv_org_abs_2507_23520
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Linear quotients, linear resolutions and the lcm-lattice
Varshavsky, Roni
Commutative Algebra
Combinatorics
Linear resolutions and the stronger notion of linear quotients are important properties of monomial ideals. In this paper, we fully characterize linear quotients in terms of the lcm-lattice of monomial ideals. We also formulate an analogous characterization for monomial ideals with linear resolutions, making explicit a relationship that is implicit in the existing literature. These results complement characterizations of these two properties in terms of the Alexander dual of the corresponding Stanley-Reisner simplicial complex. In addition, we discuss applications to the case of edge ideals.
title Linear quotients, linear resolutions and the lcm-lattice
topic Commutative Algebra
Combinatorics
url https://arxiv.org/abs/2507.23520