When the positivity of the h-vector implies the Cohen-Macaulay property

We study relations between the Cohen-Macaulay property and the positivity of $h$-vectors, showing that these two conditions are equivalent for those locally Cohen-Macaulay equidimensional closed projective subschemes $X$, which are close to a complete intersection $Y$ (of the same codimension) in terms of the difference between the degrees. More precisely, let $X\subset \mathbb P^n_K$ ($n\geq 4$) be contained in $Y$, either of codimension two with $deg(Y)-deg(X)\leq 5$ or of codimension $\geq 3$ with $deg(Y)-deg(X)\leq 3$. Over a field $K$ of characteristic 0, we prove that $X$ is arithmetically Cohen-Macaulay if and only if its $h$-vector is positive, improving results of a previous work. We show that this equivalence holds also for space curves $C$ with $deg(Y)-deg(C)\leq 5$ in every characteristic $ch(K)\neq 2$. Moreover, we find other classes of subschemes for which the positivity of the $h$-vector implies the Cohen-Macaulay property and provide several examples.Comment: Main changes with respect the previuos version are in the title, the abstract, the introduction and the bibliograph

E-learning as a tool for the recovery and promotion of meta-cognitive and affective aspects in university teaching

Questo lavoro descrive i risultati di una sperimentazione didattica condotta su un gruppo di studenti dei corsi di ingegneria dell'Università Parthenope di Napoli. Tali studenti non avevano sostenuto l'esame obbligatorio di "Algebra e Geometria" previsto al primo anno dell’ordinamento didattico.Le principali ragioni di tale fallimento sono state identificate in fattori affettivi e metacognitivi, nel metodo di studio basato sulla memorizzazione piuttosto che sulla comprensione e nell'ap-proccio procedurale nella risoluzione degli esercizi. Al fine di supportare tali studenti nello studio della disciplina e di condurli al superamento dell’esame è stato progettato e realizzato un corso di recupero. In tale contesto al fine di valorizzare gli aspetti emotivi e metacognitivi dell'apprendimento, sono state progettate lezioni ad hoc, e ideate singole attività che prevede-vano la valutazione tra pari, fatte avvalendosi dello strumento workshop della piattaforma moodle.La valutazione tra pari, infatti, migliora l'apprendimento degli studenti sviluppando metacogni-zione e pensiero critico. Inoltre, l'uso del computer avvicina gli studenti alla materia perché grazie alla loro giovane età, lo riconoscono come strumento famigliare. L'uso delle piattaforme di e-learning ha anche un aspetto sociale: grazie all'uso delle comunità di apprendimento, la comprensione di un argomento diventa anche il risultato di un processo comunitario.I risultati dell'intervento sono stati mediamente positivi. Molti studenti sono riusciti a superare l'esame ed hanno mostrato più piacere nello studio nonché una conoscenza più profonda degli argomenti. Le criticità osservate sono state legate a problemi tecnici e alla mancanza di impe-gno e di costanza di alcuni studenti non sempre in grado di gestire bene i loro tempi

Singular hypersurfaces characterizing the Lefschetz properties

In the paper untitled "Laplace equations and the Weak Lefschetz Property" the authors highlight the link between rational varieties satisfying a Laplace equation and artinian ideals that fail the Weak Lefschetz property. Continuing their work we extend this link to the more general situation of artinian ideals failing the Strong Lefschetz Property. We characterize the failure of SLP (that includes WLP) by the existence of special singular hypersurfaces (cones for WLP). This characterization allows us to solve three problems posed by Migliore and Nagel and to give new examples of ideals failing the SLP. Finally, line arrangements are related to artinian ideals and the unstability of the associated derivation bundle is linked with the failure of SLP. Moreover we reformulate the so-called Terao's conjecture for free line arrangements in terms of artinian ideals failing the SLP

The equations of space curves on a quadric

The homogeneous ideals of curves in a double plane have been studied by Chiarli, Greco, Nagel. Completing this work we describe the equations of any curve that is contained in some quadric. As a consequence, we classify the Hartshorne-Rao modules of such curves

Laplace equations, Lefschetz properties and line arrangements

In this note we generalize the main result in the previous work on JLMS on artinian ideals failing Lefschetz properties, varieties satisfying Laplace equations and existence of suitable singular hypersurfaces. Moreover we characterize the minimally generation of ideals generated by power of linear forms by the conguration of their dual points in the projective plane. Finally we show the equivalence among failing SLP, Laplace equations and unexpected curves

Corruption and policy-making. How corrupt models favor the mafias. The case study of Italy

Based on empirical research focused on the phenomenon of corruption in Italy. The purpose of the contribution is to show the different models that are made of corruption pacts according to the actors who regulate them. The basis of the judicial documents was provided by the National Anti-Mafia Directorate (DNAA), the Court of Auditors, and a sample of Courts of Appeal from different jurisdictional districts. The information collected offers an account of the influence that the various mafias have on public policies and the ability to circumvent current legislation. The contribution underlines the existing interpretative limits and why they do not explain to what extent great and small corruption are related

The Hartshorne-Rao module of curves on rational normal scrolls

We study the Hartshorne-Rao module of curves lying on a rational normal scroll S_e of invariant e ≥ 0 in P^{e+3} .We calculate the Rao function, we characterize the aCM curves on S_e .Finally, we give an algorithm to check if a curve is aC M or not and, inthe second case, to calculate the Rao function

Training Language Mediators and Interpreters through Embodied Cognition, Immersive Learning and Virtual Reality: Didactic, Organizational and Cost Benefits

The use of Virtual Reality (VR) for training purposes has expanded exponentially in the last decade. This paper specifically examines the use of VR in the training of language mediators and interpreters. By way of exemplification, the paper describes a training project at the University of Palermo, the “Coopera” project. The physically-cognitively immersive ‘learning by doing’ factor that characterizes a VR educational experience is particularly well-suited to skill- based activities. The paper explains how the immersive nature of VR and the notion of ‘embodied cognition’ is particularly suited to mediator/interpreter training by plausibly reproducing daily life situations and providing a ‘risk- free’ environment in which students can safely practice (and make mistakes) without causing harm to themselves and others, and also to contain the high costs of mediator/interpreter training. We hope the Coopera project will help foster further research into new technologies in immersive language-mediation pedagogy