The Waldschmidt Constant of Squarefree Monomial Ideals

Abstract

The last two chapters introduced the Waldschmidt constant of a homogeneous ideal of set of (fat) points and some of its properties. In fact, the definition of the Waldschmidt constant makes sense for any homogeneous ideal. In this chapter we explain how to compute this invariant in the case of squarefree monomial ideals. In the case of edge ideals, we will also give a combinatorial interpretation of this invariant. Throughout this chapter, $R = \mathbb {K}[x_1,\ldots ,x_n]$ is a polynomial ring over a field $\mathbb {K}$, where $\mathbb {K}$ has characteristic zero and is algebraically closed. All ideals I ⊆ R will be assumed to be homogeneous, and in most cases, I will be a squarefree monomial ideal.