KW Semigroups -- Their Betti Numbers, Apéry Posets and Tangent Cones

Fuente: arXiv
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Main Authors: González-Sánchez, Mario, Srinivasan, Hema
Format: Preprint
Published: 2026
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_version_ 1866910260722139136
author González-Sánchez, Mario
Srinivasan, Hema
author_facet González-Sánchez, Mario
Srinivasan, Hema
contents Let p<q be coprime integers. Kunz-Waldi semigroups are numerical semigroups containing p and q and contained in <p,q,r>, where 2r=p,q,p+q whichever is even. In this paper, we prove a conjecture on the Betti numbers of the semigroup rings of these semigroups, showing that they coincide with those of the ideal of 2x2 minors of a 2xn generic matrix, where n is the embedding dimension. Moreover, we characterize the Apéry posets of Kunz-Waldi semigroups and determine when their tangent cones are Cohen-Macaulay.
format Preprint
id arxiv_https___arxiv_org_abs_2605_27035
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle KW Semigroups -- Their Betti Numbers, Apéry Posets and Tangent Cones
González-Sánchez, Mario
Srinivasan, Hema
Commutative Algebra
13D02, 13A30, 20M14
Let p<q be coprime integers. Kunz-Waldi semigroups are numerical semigroups containing p and q and contained in <p,q,r>, where 2r=p,q,p+q whichever is even. In this paper, we prove a conjecture on the Betti numbers of the semigroup rings of these semigroups, showing that they coincide with those of the ideal of 2x2 minors of a 2xn generic matrix, where n is the embedding dimension. Moreover, we characterize the Apéry posets of Kunz-Waldi semigroups and determine when their tangent cones are Cohen-Macaulay.
title KW Semigroups -- Their Betti Numbers, Apéry Posets and Tangent Cones
topic Commutative Algebra
13D02, 13A30, 20M14
url https://arxiv.org/abs/2605.27035