Zobrazeno 1 - 10
of 75
pro vyhledávání: '"STRAZZANTI, FRANCESCO"'
We describe the canonical module of a simplicial affine semigroup ring $\mathbb{K}[S]$ and its trace ideal. As a consequence, we characterize when $\mathbb{K}[S]$ is nearly Gorenstein in terms of arithmetic properties of the semigroup $S$. Then, we f
Externí odkaz:
http://arxiv.org/abs/2411.12081
Several algebraic properties of a binomial edge ideal $J_G$ can be interpreted in terms of combinatorial properties of its associated graph $G$. In particular, the so-called cut-point sets of a graph $G$, special sets of vertices that disconnect $G$
Externí odkaz:
http://arxiv.org/abs/2306.17076
Publikováno v:
Research in the Mathematical Sciences 9 (2022), Article number: 40
In this survey paper we first present the main properties of sequentially Cohen-Macaulay modules. Some basic examples are provided to help the reader with quickly getting acquainted with this topic. We then discuss two generalizations of the notion o
Externí odkaz:
http://arxiv.org/abs/2304.06609
A combinatorial property that characterizes Cohen-Macaulay binomial edge ideals has long been elusive. A recent conjecture ties the Cohen-Macaulayness of a binomial edge ideal $J_G$ to special disconnecting sets of vertices of its underlying graph $G
Externí odkaz:
http://arxiv.org/abs/2212.09181
We explore the dependence of the Betti numbers of monomial ideals on the characteristic of the field. A first observation is that for a fixed prime $p$ either the $i$-th Betti number of all high enough powers of a monomial ideal differs in characteri
Externí odkaz:
http://arxiv.org/abs/2201.00571
We characterize when the monomial maximal ideal of a simplicial affine semigroup ring has a monomial minimal reduction. When this is the case, we study the Cohen-Macaulay and Gorenstein properties of the associated graded ring and provide several bou
Externí odkaz:
http://arxiv.org/abs/2107.09970
The cut sets of a graph are special sets of vertices whose removal disconnects the graph. They are fundamental in the study of binomial edge ideals, since they encode their minimal primary decomposition. We introduce the class of accessible graphs as
Externí odkaz:
http://arxiv.org/abs/2101.03619
Publikováno v:
In Journal of Algebra 15 January 2024 638:189-213
We investigate the nearly Gorenstein property among $d$-dimensional cyclic quotient singularities $\Bbbk[[x_1,\dots,x_d]]^G$, where $\Bbbk$ is an algebraically closed field and $G\subseteq{\rm GL}(d,\Bbbk)$ is a finite small cyclic group whose order
Externí odkaz:
http://arxiv.org/abs/2006.03457
Autor:
D'Anna, Marco, Strazzanti, Francesco
Given a one-dimensional Cohen-Macaulay local ring $(R,\mathfrak{m},k)$, we prove that it is almost Gorenstein if and only if $\mathfrak{m}$ is a canonical module of the ring $\mathfrak{m}:\mathfrak{m}$. Then, we generalize this result by introducing
Externí odkaz:
http://arxiv.org/abs/2004.02252