Squarefree Lexsegment Ideals with Linear Resolution

Bonanzinga, Vittoria; Sorrenti, Loredana

Bonanzinga, Vittoria ; Sorrenti, Loredana

Bollettino dell'Unione Matematica Italiana, Tome 1 (2008), p. 275-291 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

In this paper we determine all squarefree completely lexsegment ideals which have a linear resolution. Let $M_{d}$ denote the set of all squarefree monomials of degree $d$ in a polynomial ring $k[x_{1},\ldots,x_{n}]$ in $n$ variables over a field $k$ . We order the monomials lexicographically such that $x_{1}>x_{2}>\ldots>x_{n}$ , thus a lexsegment (of degree $d$ ) is a subset of $M_{d}$ of the form $L(u,v)=\{w\in M_{d}:u\geq w\geq v\}$ for some $u,v\in M_{d}$ con $u\geq v$ . An ideal generated by a lexsegment is called a lexsegment ideal. We describe the procedure to determine when such an ideal has a linear resolution.

In questo articolo determiniamo tutti gli ideali completamente lexsegmento squarefree con risoluzione lineare. Sia $M_{d}$ l'insieme di tutti i monomi squarefree di grado $d$ in un anello di polinomi $k[x_{1},\ldots,x_{n}]$ in $n$ variabili su un campo $k$ . Ordiniamo i monomi lessicograficamente in modo che $x_{1}>x_{2}>\ldots>x_{n}$ , così un lexsegmento (di grado $d$ ) è un sottoinsieme di $M_{d}$ del tipo $L(u,v)=\{w\in M_{d}:u\geq w\geq v\}$ per qualche $u,v\in M_{d}$ con $u\geq v$ . Un ideale generato da un lexsegmento è chiamato ideale lexsegmento. Descriviamo la procedura per determinare quando un tale ideale ha risoluzione lineare.

Publié le : 2008-02-01

MR 2424294 | Zbl 1164.13009

@article{BUMI_2008_9_1_1_275_0,
     author = {Vittoria Bonanzinga and Loredana Sorrenti},
     title = {Squarefree Lexsegment Ideals with Linear Resolution},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {1},
     year = {2008},
     pages = {275-291},
     zbl = {1164.13009},
     mrnumber = {2424294},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2008_9_1_1_275_0}
}

Bonanzinga, Vittoria; Sorrenti, Loredana. Squarefree Lexsegment Ideals with Linear Resolution. Bollettino dell'Unione Matematica Italiana, Tome 1 (2008) pp. 275-291. http://gdmltest.u-ga.fr/item/BUMI_2008_9_1_1_275_0/

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