Some well-known arithmetically Cohen-Macaulay configurations of linear varieties in Pr as k-configurations, partial intersections and star configurations are generalized by introducing tower schemes. Tower schemes are reduced schemes that are a finite union of linear varieties whose support set is a suitable finite subset of Z+c called tower set. We prove that the tower schemes are arithmetically Cohen-Macaulay and we compute their Hilbert function in terms of their support. Afterwards, since even in codimension 2 not every arithmetically Cohen-Macaulay squarefree monomial ideal is the ideal of a tower scheme, we slightly extend this notion by defining generalized tower schemes (in codimension 2). Our main result consists in showing that the support of these configurations (the generalized tower set) gives a combinatorial characterization of the primary decomposition of the arithmetically Cohen-Macaulay squarefree monomial ideals.

Tower sets and other configurations with the Cohen-Macaulay property / Favacchio, G.; Ragusa, A.; Zappala, G.. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - STAMPA. - 219:6(2015), pp. 2260-2278. [10.1016/j.jpaa.2014.07.035]

Tower sets and other configurations with the Cohen-Macaulay property

Favacchio G.;
2015

Abstract

Some well-known arithmetically Cohen-Macaulay configurations of linear varieties in Pr as k-configurations, partial intersections and star configurations are generalized by introducing tower schemes. Tower schemes are reduced schemes that are a finite union of linear varieties whose support set is a suitable finite subset of Z+c called tower set. We prove that the tower schemes are arithmetically Cohen-Macaulay and we compute their Hilbert function in terms of their support. Afterwards, since even in codimension 2 not every arithmetically Cohen-Macaulay squarefree monomial ideal is the ideal of a tower scheme, we slightly extend this notion by defining generalized tower schemes (in codimension 2). Our main result consists in showing that the support of these configurations (the generalized tower set) gives a combinatorial characterization of the primary decomposition of the arithmetically Cohen-Macaulay squarefree monomial ideals.
File in questo prodotto:
File Dimensione Formato  
postprint-editoriale Tower sets and other configurations with the Cohen–Macaulay property.pdf

non disponibili

Descrizione: Articolo principale
Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 459.76 kB
Formato Adobe PDF
459.76 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
arxiv-preprint-1401.3535.pdf

accesso aperto

Tipologia: 1. Preprint / submitted version [pre- review]
Licenza: PUBBLICO - Tutti i diritti riservati
Dimensione 251.42 kB
Formato Adobe PDF
251.42 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2859964