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In this work we define, for the first time, the affine and projective plane over the real Okubo algebra, showing a concrete geometrical interpretation of its Spin group. Okubo algebra is a flexible, composition algebra which is also a not unital division algebra. Even though Okubo algebra has been known for more than 40 years, we believe that this is the first time the algebra was used for affine and projective geometry. After showing that all axioms of affine geometry are verified, we define a projective plane over Okubo algebra as completion of the affine plane and directly through the use of Veronese coordinates. We then present a bijection between the two constructions. Finally we show a geometric interpretation of Spin(O) as the group of collineations that preserve the axis of the plane., Comment: 13 pages, 2 figures

L’étude propose une réévaluation du sémantisme des motifs solaires et des effets d’ensoleillement que Nicolas Poussin a peints dans un Moïse sauvé des eaux destiné au soyeux Jean Pointel. À partir d’une observation rapprochée de la composition qu’éclairent aussi la poésie et l’exégèse relatives à la découverte de Moïse, on tâche de montrer comment le chromatisme et la disposition des personnages et des parerga (éléments du décorum) aboutissent à une réinvention sublime du sujet, présenté comme la naissance d’un astre providentiel qui dissipe les ténèbres de la religion païenne égyptienne et présage l’avènement du monothéisme chrétien en tant que figure du Christ Soleil de Justice, étoile brillante du matin et Verbe lumière. Mots-clés : Nicolas Poussin, Véronèse, Saint-Amant, Jean Auvray, Nicolas Talon, figure, fond, chromatisme, Bible, exégèse, sublime, iconologie. The discovery of Moses on the banks of the Nile according to Nicolas Poussin in 1647 This study proposes a reevaluation of the semantics of the solar motifs and sunlight effects that Nicolas Poussin included in a depiction of Moses Saved from the Waters, produced for the silk merchant Jean Pointel. Based on a close observation of the composition, which is also illuminated by the poetry and exegesis relating to the discovery of Moses, we try to show how the chromaticism and the arrangement of characters and decorum lead to a sublime reinvention of the subject, presented as the birth of a providential star that dispels the darkness of the Egyptian pagan religion and augurs the advent of Christian monotheism in the figure of Christ Sun of Justice, the shining morning star, and the Word of Light. Keywords: Nicolas Poussin, Veronese, Saint-Amant, Jean Auvray, Nicolas Talon, figure, background, chromaticism, Bible, exegesis, sublime, iconology.

La ricerca esamina l’impalcato delle prospettive architettoniche realizzate da Paolo Caliari (Veronese) in due tipologie di teleri veneziani per comprendere le modalità che governano gli sfondati di queste pitture. Dopo aver delineato l’ambito culturale entro il quale il maestro operava, il modus operandi della sua bottega, e vagliato i contenuti dei trattati prospettici coevi, lo studio analizza la geometria dei teleri dipinti dal pittore per refettori e chiese per poi approfondire l’indagine in due casi studio: il Convito in casa di Levi (1573) e l’Apoteosi di Venezia (1582).

At the turn of the sixteenth century, a series of striking portraits emerged in Northern Italy. Patrons, once confined to the independent likeness or sacra conversazione, began to commemorate themselves anew in scenes from the life of Christ. From the Nativity to Calvary, individuals appear in variable landscapes without intercessory saint or any mode of physical demarcation. Although these portraits came to characterize the work of celebrated Veneto artists, scholars have yet to establish their origin and evolving significance. My dissertation offers the first systematic study on this iconographic pattern I term the visionary portrait.

L’obiettivo della ricerca è esaminare l’impalcato delle prospettive architettoniche realizzate da Paolo Caliari (detto il Veronese) in due tipologie di teleri veneziani per comprendere le modalità che governano gli sfondati di queste celebri pitture. Dopo aver delineato l’ambito culturale entro il quale il maestro operava, la metodica esecutiva della sua bottega, e considerato i contenuti dei trattati prospettici coevi, lo studio esamina la geometria dei teleri dipinti dal pittore per refettori e chiese, per poi approfondire l’indagine in due casi studio – il Convito in casa di Levi (1573) e l’Apoteosi di Venezia (1582) – verificando in ambiente digitale i dispositivi dedotti in queste opere attraverso gli esiti delle operazioni di inversione prospettica e di modellazione stereometrica. I risultati ottenuti dall’indagine contribuiscono ad attestare le cognizioni del Veronese in materia prospettica, e la perizia con la quale spesso egli infrangeva celatamente il rigore del metodo per riprodurre efficaci illusioni spaziali. Alcune considerazioni emerse dall’analisi del bozzetto dell’Apoteosi di Venezia e dai soffittali sottoposti a disamina hanno anche consentito di ipotizzare l’impiego di un sistema diretto di costruzione prospettica da parte dell’officina Caliari.

The second Veronese ideal $I_n$ contains a natural complete intersection $J_n$ generated by the principal $2$-minors of a symmetric $(n\times n)$-matrix. We determine subintersections of the primary decomposition of $J_n$ where one intersectand is omitted. If $I_n$ is omitted, the result is the other end of a complete intersection link as in liaison theory. These subintersections also yield interesting insights into binomial ideals and multigraded algebra. For example, if $n$ is even, $I_n$ is a Gorenstein ideal and the intersection of the remaining primary components of $J_n$ equals $J_n+\langle f \rangle$ for an explicit polynomial $f$ constructed from the fibers of the Veronese grading map., 12 pages

International audience; Despite of their deep attachment to the traditional standards still in use for the representation of Christian figures, the Armenian artists take up progressively Western patterns in the 17th and 18th centuries. With the help of some concrete examples from various artistic sources, the author describes the development of narrative contents in religious paintings in the New Julfa community and the dissemination of a renewed aesthetic expression towards the Armenian Diaspora in different countries.

In this article the author discusses the works known in Spain by Alvise Benfatto del Friso and Michèle Parrasio and also attributes some paintings to them for the first time.En este artículo se estudian tanto las obras conocidas en España de Alvise Benfatto del Friso y de Michele Parrasio como otras que se les atribuye por primera vez.

The dynamics of tetraploidy with mixed mating are studied, with fitness of inbreeders as a parameter. We determine the fixed points and the asymptotic behavior of the trajectories in the gametic and zygotic structures associated to this reproductive system. Our methods include elementary commutative algebra and algebraic geometry, and we make pervasive use of the computer program Macaulay2.

During his first period in Paris (1910-1914), the russian painter Marc Chagall met, most of all at the Louvre Museum, the masters of western painting, as he wrote in “My life”, his autobiography.The case in study, which is the influence of the artist Paolo Caliari in the artwork of the russian painter, reveals the fact that even though historiography has overlooked the quotes of artists present in ‘My life’, it’s interpretation under the concept of tradition of Ernst Gombrich shows the relevance that the russian gave to the artworks he met at the french capital, proposing an alternative vision to the idea of the rebel and vanguardist artist that was created around Chagall’s figure in the twentieth century. Durante su primera estadía en París (1910-1914), el pintor ruso Marc Chagall conoció, principalmente en el museo del Louvre, a los maestros de la pintura occidental, tal como registró en Mi vida, su autobiografía.El caso aquí estudiado, la influencia del artista italiano Paolo Caliari en el trabajo del ruso, revela que aunque la historiografía ha pasado por alto las citas a artistas presentes en Mi vida, su lectura a la luz del concepto de tradición de Ernst Gombrich demuestra la importancia que el ruso le otorgó a las obras que conoció en la capital francesa, proponiendo una visión alternativa a la idea de artista rebelde y vanguardista que durante el siglo XX se elaboró en torno a la figura de Chagall.

International audience; We give a partial ''~quasi-stratification~'' of the secant varieties of the order $d$ Veronese variety $X_{m,d}$ of $\mathbb {P}^m$. It covers the set $\sigma _t(X_{m,d})^{\dagger}$ of all points lying on the linear span of curvilinear subschemes of $X_{m,d}$, but two ''~quasi-strata~'' may overlap. For low border rank two different ''~quasi-strata~'' are disjoint and we compute the symmetric rank of their elements. Our tool is the Hilbert schemes of curvilinear subschemes of Veronese varieties. To get a stratification we attach to each $P\in \sigma _t(X_{m,d})^{\dagger}$ the minimal label of a quasi-stratum containing it.

Let $X_{m,d}\subset \mathbb {P}^N$, $N:= \binom{m+d}{m}-1$, be the order $d$ Veronese embedding of $\mathbb {P}^m$. Let $\tau (X_{m,d})\subset \mathbb {P}^N$, be the tangent developable of $X_{m,d}$. For each integer $t \ge 2$ let $\tau (X_{m,d},t)\subseteq \mathbb {P}^N$, be the joint of $\tau (X_{m,d})$ and $t-2$ copies of $X_{m,d}$. Here we prove that if $m\ge 2$, $d\ge 7$ and $t \le 1 + \lfloor \binom{m+d-2}{m}/(m+1)\rfloor$, then for a general $P\in \tau (X_{m,d},t)$ there are uniquely determined $P_1,...,P_{t-2}\in X_{m,d}$ and a unique tangent vector $\nu$ of $X_{m,d}$ such that $P$ is in the linear span of $\nu \cup \{P_1,...,P_{t-2}\}$, i.e. a degree $d$ linear form $f$ associated to $P$ may be written as $$f = L_{t-1}^{d-1}L_t + \sum_{i=1}^{t-2} L_i^d$$ with $L_i$, $1 \le i \le t$, uniquely determined (up to a constant) linear forms on $\mathbb {P}^m$., Comment: 7 pages

International audience

Recenzija, prikaz izložbe "Tizian, Tintoretto, Veronese – veliki majstori renesanse", Galerija Klovićevi dvori, Zagreb, 22. studeni 2011. – 22. siječanj 2012.

If $X\subset \mathbb{P}^n$ is a projective non degenerate variety, the $X$-rank of a point $P\in \mathbb{P}^n$ is defined to be the minimum integer $r$ such that $P$ belongs to the span of $r$ points of $X$. We describe the complete stratification of the fourth secant variety of any Veronese variety $X$ via the $X$-rank. This result has an equivalent translation in terms both of symmetric tensors and homogeneous polynomials. It allows to classify all the possible integers $r$ that can occur in the minimal decomposition of either a symmetric tensor or a homogeneous polynomial of $X$-border rank 4 (i.e. contained in the fourth secant variety) as a linear combination of either completely decomposable tensors or powers of linear forms respectively., In Press: Advances in Pure and Applied Mathematics

Nel contributo si sottopone ad esame il celebre passo gaiano (Gai IV 2) contenente la definizione di actio in personam e di actio in rem. Dopo un'analisi delle numerose letture proposte dai principali Editori delle Institutiones e delle emendazioni proposte dalla Dottrina, verificando quali altre fonti siano state messe a partito per integrare il testo gaiano (con particolare riferimento alle Istituzioni di Giustiniano e alla Parafrasi di Teofilo) viene compiuta una verifica delle trascrizioni del folium 52r contenute negli apografi di Böcking e di Studemund, eseguendo un'analisi paleografica d tale folium. Grazie all'impiego delle più moderne tecniche di Text recovery (Multispectral Imaging UV//IR) si giunge così ad una nuova e più corretta lettura del passo delle Institutiones di Gaio (IV, 2).

Autor donosi sintetski tekst o renesansnom slikarstvu talijanskih majstora u Hrvatskoj i analizu najvredniji pojedinačnih umjetničkih djela.