Support posets of some monomial ideals

2020/09/17 by Pascual-Ortigosa, Patricia, Sáenz-de-Cabezón, Eduardo · 1 citation
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.08125

Abstract

The support poset of a monomial ideal I\subseteqk[x₁,…,x_n] encodes the relation between the variables x₁,…,x_n and the minimal monomial generators of I. It is known that not every poset is realizable as the support poset of some monomial ideal. We describe some posets P for which we can explicitly find at least one monomial ideal I_P such that P is the support poset of I_P. Also, for some families of monomial ideals we describe their support posets and study their properties. As an example of application we examine the relation between forests and series-parallel ideals.

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