Squarefree Lexsegment Ideals with Linear Resolution

Bonanzinga, Vittoria ; Sorrenti, Loredana

Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 1, pp. 275-291

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.