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In this work we study line arrangements consisting in lines passing through three non-aligned points. We call them triangular arrangements. We prove that any combinatorics of a triangular arrangement is always realized by a Roots-of-Unity-Arrangement, which is a particular class of triangular arrangements. Among these Roots-of Unity-Arrangements, we provide conditions that ensure their freeness. Finally, we give two triangular arrangements having the same weak combinatorics, such that one is free but the other one is not. [ABSTRACT FROM AUTHOR]

We prove stability of logarithmic tangent sheaves of singular hypersurfaces |$D$| of the projective space with constraints on the dimension and degree of the singularities of |$D$|⁠. As the main application, we prove that determinants and symmetric determinants have simple (in characteristic zero, stable) logarithmic tangent sheaves and we describe an open dense piece of the associated moduli space. [ABSTRACT FROM AUTHOR]

Over the past forty years many papers have studied logarithmic sheaves associated to reduced divisors, in particular logarithmic bundles associated to plane curves. An interesting family of these curves are the so-called free ones for which the associated logarithmic sheaf is the direct sum of two line bundles. Terao conjectured thirty years ago that when a curve is a finite set of distinct lines (i.e. a line arrangement) its freeness depends solely on its combinatorics, but this has only been proved for sets of up to 12 lines. In looking for a counter-example to Terao's conjecture, the nearly free curves introduced by Dimca and Sticlaru arise naturally. We prove here that the logarithmic bundle associated to a nearly free curve possesses a minimal non-zero section that vanishes on one single point, P say, called the jumping point, and that this characterises the bundle. We then give a precise description of the behaviour of P. Based on detailed examples we then show that the position of P relative to its corresponding nearly free arrangement of lines may or may not be a combinatorial invariant, depending on the chosen combinatorics. [ABSTRACT FROM AUTHOR]

This essay addresses one specific element of Decameron I.1, the curious order in which the holy friar questions Ciappelletto in his confession, and relates it to the larger dialogue Boccaccio establishes with Dante's Commedia. By avoiding the canonical models of confessing penitents, which traditionally unfolded according to the Decalogue, the seven deadly sins, or the sinner's circumstances, the confession proceedings in the first novella evoke most distinctively and idiosyncratically the order of sins in Dante's hell. Dante's authoritative but not canonical text about the Christian afterlife, thus, colors our reading of the first novella of the new work, in which the protagonist, narrator, and author are all similarly involved in the making of a fiction. [ABSTRACT FROM AUTHOR]

The goal of this paper is to prove the existence of indecomposable rank [ABSTRACT FROM AUTHOR]

Let be an integral and projective curve whose canonical model lies on a rational normal scroll of dimension . We mainly study some properties on , such as gonality and the kind of singularities, in the case where and is non-Gorenstein, and in the case where , the scroll is smooth, and is a local complete intersection inside . We also prove that the canonical model of a rational monomial curve with just one singular point lies on a surface scroll if and only if the gonality of the curve is at most , and that it lies on a threefold scroll if and only if the gonality is at most . [ABSTRACT FROM AUTHOR]

In this work, we will prove results that ensure the simplicity and the exceptionality of vector bundles, which are defined by the splitting of pure resolutions. We will call such objects syzygy bundles. [ABSTRACT FROM AUTHOR]

In this work we introduce the definition of Schwarzenberger bundle on a Grassmannian. Recalling the notion of Steiner bundle, we generalize the concept of jumping pair for a Steiner bundle on a Grassmannian. After studying the jumping locus variety and bounding its dimension, we give a complete classification of Steiner bundles with jumping locus of maximal dimension, which all are Schwarzenberger bundles. [ABSTRACT FROM AUTHOR]

An essay is presented on the aspects to consider when attempting to gloss a literary work such as "Decameron," by Giovanni Boccaccio. It explores the conditions required to bring a different text to its interpretation and the merit of the gloss. It analyzes the parameters determining the intertextual dynamics of the book. It examines how the book resonates with the voice of another intertext.