arXiv subjects

Liena Colarte

Publications and source records attributed to Liena Colarte.

2 recordsLinked to original sources

arXiv2021

Hypertetrahedral arrangements

In this paper, we introduce the notion of a complete hypertetrahedral arrangement $\mathcal{A}$ in $\mathbb{P}^{n}$. We address two basic problems. First, we describe the local freeness of $\mathcal{A}$ in terms of smaller complete hypertetrahedral arrangements and graph theory properties, specializing the Mustaţă-Schenck criterion. As an application, we obtain that general complete hypertetrahedral arrangements are not locally free. In the second part of this paper, we bound the initial degree of the first syzygy module of the Jacobian ideal of $\mathcal{A}$.

math.AG↗

arXiv2018

On the Coefficients of the Permanent and the Determinant of a Circulant Matrix. Applications

Let $d(N )$ (resp. $p(N )$) be the number of summands in the determinant (resp. permanent) of an $N\times N$ circulant matrix $A = (a_{ij} )$ given by $a_{ij} = X_{i+j}$ where $i + j$ should be considered $\mod N$ . This short note is devoted to prove that $d(N ) = p(N )$ if and only if $N$ is a prime power. We then give an application to homogeneous monomial ideals failing the Weak Lefschetz property.

math.AG↗