arXiv subjects

Beatrice Picone

Publications and source records attributed to Beatrice Picone.

2 recordsLinked to original sources

arXiv2018

Regularity of bicyclic Graphs and their powers

Let $I(G)$ be the edge ideal of a bicyclic graph. In this paper, we characterize the Castelnuovo-Mumford regularity of $I(G)$ in terms of the induced matching number of $G$. For the base case of this family of graphs, i.e. dumbbell graph, we explicitly compute the induced matching number. Moreover, we prove that $ \operatorname{reg}(I(G)^q)=2q+\operatorname{reg}(I(G))-2$, for all $ q\geq 1 $, when $ G $ is a dumbbell graph with a connecting path having no more than two vertices.

math.AC↗

arXiv2018

Special arrangements of lines: codimension two ACM varieties in $\mathbb P^1\times\mathbb P^1\times\mathbb P^1$

In this paper we investigate special arrangements of lines in multiprojective spaces. In particular, we characterize codimensional two arithmetically Cohen-Macaulay (ACM) varieties in $\mathbb P^1\times\mathbb P^1\times\mathbb P^1$, called varieties of lines. We also describe their ACM property from combinatorial algebra point of view.

math.AG↗