Nous allons étudier les propriétés des courbes algébriques sur des surfaces K3 spéciales, du point de vue de la théorie de Brill-Noether.La démonstration de Lazarsfeld du théorème de Gieseker-Petri a mis en lumière l'importance de la théorie de Brill-Noether des courbes admettant un plongement dans une surface K3. Nous allons donner une démonstration détaillée de ce résultat classique, inspirée par les idées de Pareschi. En suite, nous allons décrire le théorème de Green et Lazarsfeld, fondamental pour tout notre travail, qui établit le comportement de l'indice de Clifford des courbes sur les surfaces K3.Watanabe a montré que l'indice de Clifford de courbes sur certaines surfaces K3, admettant un recouvrement double des surfaces de del Pezzo, est calculé en utilisant les involutions non-symplectiques. Nous étudions une situation similaire pour des surfaces K3 avec un réseau de Picard isomorphe à U(m), avec m>0 un entier quelconque. Nous montrons que la gonalité et l'indice de Clifford de toute courbe lisse sur ces surfaces, avec une seule exception déterminée explicitement, sont obtenus par restriction des fibrations elliptiques de la surface. Ce travail est basé sur l'article suivant :M. Ramponi, Gonality and Clifford index of curves on elliptic K3 surfaces with Picard number two, Archiv der Mathematik, 106(4), p. 355–362, 2016.Knutsen et Lopez ont étudié en détail la théorie de Brill-Noether des courbes sur les surfaces d'Enriques. En appliquant leurs résultats, nous allons pouvoir calculer la gonalité et l'indice de Clifford de toute courbe lisse sur les surfaces K3 qui sont des recouvrements universels d'une surface d'Enriques. Ce travail est basé sur l'article suivant :M. Ramponi, Special divisors on curves on K3 surfaces carrying an Enriques involution, Manuscripta Mathematica, 153(1), p. 315–322, 2017. / We study the properties of algebraic curves lying on special K3 surfaces, from the viewpoint of Brill-Noether theory.Lazarsfeld's proof of the Gieseker-Petri theorem has revealed the importance of the Brill-Noether theory of curves which admit an embedding in a K3 surface. We give a proof of this classical result, inspired by the ideas of Pareschi. We then describe the theorem of Green and Lazarsfeld, a key result for our work, which establishes the behaviour of the Clifford index of curves on K3 surfaces.Watanabe showed that the Clifford index of curves lying on certain special K3 surfaces, realizable as a double covering of a smooth del Pezzo surface, can be determined by a direct use of the non-simplectic involution carried by these surfaces. We study a similar situation for some K3 surfaces having a Picard lattice isomorphic to U(m), with m>0 any integer. We show that the gonality and the Clifford index of all smooth curves on these surfaces, with a single, explicitly determined exception, are obtained by restriction of the elliptic fibrations of the surface. This work is based on the following article:M. Ramponi, Gonality and Clifford index of curves on elliptic K3 surfaces with Picard number two, Archiv der Mathematik, 106(4), p. 355-362, 2016.Knutsen and Lopez have studied in detail the Brill-Noether theory of curves lying on Enriques surfaces. Applying their results, we are able to determine and compute the gonality and Clifford index of any smooth curve lying on the general K3 surface which is the universal covering of an Enriques surface. This work is based on the following article:M. Ramponi, Special divisors on curves on K3 surfaces carrying an Enriques involution, Manuscripta Mathematica, 153(1), p. 315-322, 2017.

Orientador: Claudia Valladão de Mattos / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Artes / Made available in DSpace on 2018-08-17T05:59:50Z (GMT). No. of bitstreams: 1 Goncalves_TatianaFecchiodaCunha_D.pdf: 15934035 bytes, checksum: afa8628c48b9d193a001ddb1e5f7d750 (MD5) Previous issue date: 2010 / Resumo: Esta tese discute a forma com a qual a representação do "louco" e da loucura foi construída nas imagens de quatro fotógrafos que realizaram ensaios fotográficos em Hospitais Psiquiátricos brasileiros no século XX - Alice Brill (1950), Leonid Streliaev (1971), Claudio Edinger (1989-90) e Claudia Martins (1997) - com o objetivo de explicitar a concepção de loucura subjacente às imagens, bem como pontuar elementos naturalizados nestas construções. Partindo da análise de conteúdo e iconográfica, da pesquisa sobre a tradição de representação do "louco" e da loucura na produção cultural imagética do ocidente, do estudo das implicações que a técnica fotográfica por si suscita, da análise história de veiculação e recepção das imagens, bem como de seus contextos culturais de produção; foi possível pontuar conceitos e pressupostos subjacentes à construção formal da representação do "louco" e da loucura nas imagens de cada um dos fotógrafos estudados. Este estudo permitiu identificar que elementos tradicionais de representação foram acessados pelos fotógrafos estudados, num movimento de perpetuação de formas tipificadas de compreender o diverso. Por outro lado, foi possível verificar que novos elementos compositivos surgiram relacionados com contextos específicos. Assim, este estudo, contribuindo para o desvelamento de formas tipificadas de representação do "louco" e da loucura, almeja representar um esforço no sentido de ampliar as possibilidades de crítica às construções imagéticas que circulam na sociedade, bem como para o questionamento de formas naturalizadas de apreensão destes sujeitos. / Abstract: This thesis discusses ways in which the representation of madmen and madness was built on images taken by four photographers who created photographic essays in Brazilian psychiatric hospitals during the twentieth-century - Alice Brill (1950), Leonid Streliaev (1971), Claudio Edinger (1989 -90) and Claudia Marshall (1997) - in order to unveil underlying social concepts about madness, while also highlighting specific elements that were naturalized in these constructions. The method was based on content analysis and iconographic research, We studied the traditional ways Western culture represents the insane in visual productions, and the implications raised by photographic techniques. We examined the history of transmission and reception of the images and the cultural contexts in which they emerged, so as to understand concepts and assumptions underlying the formal construction of the representation of the mad in the images of the photographers that were selected for this study. The results showed that traditional elements were accessed by the photographers, as a means of perpetuating characteristic modes of understanding diversity. Nevertheless, we observed that new compositional elements emerged, related to specific contexts. By questioning the naturalized ways that society has come to apprehend madness, by critically discussing the construction of images of madmen that circulate in society, our aim was to contribute to the unveiling of typified forms of representation of the mad and madness. / Doutorado / Artes / Doutor em Artes

Seit W. Diffie und M. Hellman im Jahr 1976 ihren Ansatz für einen sicheren kryptographischen Schlüsselaustausch vorgestellten, ist der sogenannte Diskrete Logarithmus zu einem zentrales Thema der Kryptoanalyse geworden. Dieser stellt eine Erweiterung des bekannten Logarithmus auf beliebige endliche Gruppen dar. In der vorliegenden Dissertation werden zwei von C. Diem eingeführte Algorithmen untersucht, mit deren Hilfe der diskrete Logarithmus in der Picardgruppe glatter, nichthyperelliptischer Kurven vom Geschlecht g > 3 bzw. g > 4 über endlichen Körpern berechnet werden kann. Beide Ansätze basieren auf der sogenannten Indexkalkül-Methode und benutzen zur Erzeugung der dafür benötigten Relationen spezielle Linearsysteme, welche durch Schneiden von ebenen Modellen der Kurve mit Geraden erzeugt werden. Um Aussagen zur Laufzeit der Algorithmen tätigen zu können, werden verschiedene Sätze über die Geometrie von Kurven bewiesen. Als zentrale Aussage wird zum einem gezeigt, dass ebene Modelle niedrigen Grades effizient berechnet werden können. Zum anderen wird bewiesen, dass sich bei genügend großem Grundkörper die Anzahl der vollständig über dem Grundkörper zerfallenden Geraden wie heuristisch erwartet verhällt. Für beide Aussagen werden dabei Familien von Kurven betrachtet und diese gelten daher uniform für alle glatten, nichthyperelliptischen Kurven eines festen Geschlechts. Die genannten Resultate führen schlussendlich zu dem Beweis einer erwarteten Laufzeit von O(q^(2-2/(g-1))) für den ersten der beiden Algorithmen, wobei q die Anzahl der Elemente im Grundkörper darstellt. Der zweite Algoritmus verbessert dies auf eine heuristische Laufzeit in O(q^(2-2/(g-2))), imdem er Divisoren von höherem Spezialiätsgrad erzeugt. Es wird bewiesen, dass dieser Ansatz für einen uniform gegen 1 konvergierenden Anteil an glatten, nichthyperelliptischen Kurven eines festen Geschlechts über Grundkörpern großer Charakteristik eine große Anzahl an Relationen erzeugt. Wiederum werden zum Beweis der zugrundeliegenden geometrischen Aussagen Familien von Kurven betrachtet, um so die Uniformität zu gewährleisten. Beide Algorithmen wurden zudem implementiert. Zum Abschluss der Arbeit werden die Ergebnisse der entsprechenden Experimente vorgestellt und eingeordnet.

In [Bri07], Bridgeland introduced the notion of stability conditions on the bounded derived category D(X) of coherent sheaves on an algebraic variety X. This topic is originally inspired by concepts in string theory and mathematical physics and has many interesting applications in algebraic geometry. In the first part of the thesis, we provide a direct proof of an important result in [Bri08, BMS16] which states there is a two dimensional family of weak Bridgeland stability conditions on the bounded derived category D(X) of coherent sheaves on a variety X. As a first application of this result, we prove an effective restriction theorem which provides sufficient conditions on a stable locally free sheaf on a projective variety such that its restriction to a hypersurface remains stable. Secondly, we extend and complete Mukai's program to reconstruct a K3 surface from a curve on that surface. We show that the K3 surface containing the curve can be obtained uniquely as a Fourier-Mukai partner of a suitable Brill-Noether locus of vector bundles on the curve.

Texte remanié de: Dissertation--Philosophische Fakultät--Göttingen--Georg-August-Universität, 2000. / Bibliogr. p. 189-199.

We study two dimension estimates regarding linear series on algebraic curves. First, we generalize the classical Brill-Noether theorem to many cases where the Brill-Noether number is negative. Second, we extend results of Eisenbud, Harris, and Komeda on the existence of Weierstrass points with certain semigroups, by refining their dimension estimate in light of combinatorial considerations. Both results are proved by constructing chains of elliptic curves, joined at pairs of points differed by carefully chosen orders of torsion, and smoothing these chains. These arguments lead to several combinatorial problems of separate interest. / Mathematics

In this thesis I consider the influence of Alice Brill's transnational background on her photographs of 1950s São Paulo. Brill was born in 1920 to a Jewish-German family. In 1934 she immigrated to São Paulo where she involved herself in local artistic circles. From 1946-47 she received a grant to study at the University of New Mexico and with the Art Students League in New York. Brill learned photography during her time in the United States, hoping to create documentary photo-essays in Brazil which she could send to American illustrated magazines. None of Brillss works were published in the United States, however, on returning to São Paulo in 1948 Brill was invited by Pietro Maria Bardi, Director of the Museu de Arte de São Paulo Assis Chateaubriand, to "record the daily life of the citizens of São Paulo". Bardi intended the photographs to be published as an homage to the city's 400th anniversary, but lacked sufficient funding to complete the volume. Brill's images of São Paulo depict the metropolis in a way unique during the period: as a space shared by multi-racial communities. While many photographers and publications metaphorically white-washed the city by depicting only its most Europeanized attributes, Brill consciously sought out underrepresented groups, specifically the burgeoning Afro-Brazilian community. Brill's point of view was shaped by her international upbringing and training: her experience as an outsider compelled her to document other outsider communities in São Paulo. She recognized the traditions of representation already in place in Brazil and manipulated familiar types in order to represent the nation's true hybridity. Influences on her work include: the long history of part-artistic, part-anthropological studies of the Brazilian people; local photographic traditions for picturing the city and its inhabitants; the European photojournalist style introduced to Brazil in 1944; and the international sensibility of Brill's patrons, the Bardis. I attempt to show how Brill balanced these considerations with her own personal understanding of Brazil as a multivalent space.

In dieser Arbeit untersuchen wir Varietäten singulärer, quadratischer Hyperflächen, die eine projektive Kurve enthalten, und effektive Divisoren im Modulraum von Kurven, die mittels verschiedener Eigenschaften von quadratischen Hyperflächen definiert werden. In Kapitel 2 berechnen wir die Klasse des effektiven Divisors im Modulraum von Kurven mit Geschlecht g und n markierten Punkten, der als der Ort von solchen markierten Kurven definiert ist, dass das Projektion der kanonischen Abbildung der Kurve von den markierten Punkten auf einer quadratischen Hyperfläche liegt. Mithilfe dieser Klasse zeigen wir, dass die Modulräume mit Geschlecht 16, 17 und 8 markierten Punkten Varietäten von allgemeinem Typ sind. In Kapitel 3 stratifizieren wir den Raum von quadratischen Hyperflächen, die eine projektive Kurve enthalten, mithilfe des Rangs dieser Hyperflächen. Wir zeigen, dass jedes Stratum die erwartete Dimension hat, falls die Kurve ein allgemeines Element des Hilbertschemas ist. Mit Rücksicht auf Rang von quadratischen Hyperflächen, eine ähnliche Konstruktion wie in Kapitel 2 ergibt neue Divisoren im Modulraum von Kurven. Wir berechnen die Klasse von diesen Divisoren und zeigen, dass der Modulraum von Kurven mit Geschlecht 15 und 9 markierten Punkten eine Varietät von allgemeinem Typ ist. In Kapitel 4 präsentieren wir unterschiedliche Resultate, die mit Themen von vorigen Kapiteln im Zusammenhang stehen. Zum Ersten berechnen wir die Klasse von Divisoren im Modulraum von Kurven, die als die Orte von Kurven definiert sind, wo die maximale Rang Vermutung nicht gilt. Zweitens zeigen wir, dass jedes Geradenbündel als Tensorprodukt von zwei Geradenbündeln mit zwei Schnitten geschrieben werden kann, falls die Kurve allgemein ist und eine gewisse numerische Bedingung erfüllt ist. Zuletzt benutzen wir bekannte Divisorklassen zu zeigen, dass der Modulraum von Kurven mit Geschlecht 12 und 10 markierten Punkten eine Varietät von allgemeinem Typ ist. / In this thesis, we study varieties of singular quadrics containing a projective curve and effective divisors in the moduli space of pointed curves defined via various constructions involving quadric hypersurfaces. In Chapter 2, we compute the class of the effective divisor in the moduli space of n-pointed genus g curves, which is defined as the locus of pointed curves such that the projection of the canonical model of the curve from the marked points lies on a quadric hypersurface. Using this class, we show that the moduli spaces of 8-pointed genus 16 and 17 curves are varieties of general type. In Chapter 3, we stratify the space of quadrics that contain a given curve in the projective space, using the ranks of the quadrics. We show, in a certain numerical range, that each stratum has the expected dimension if the curve is general in its Hilbert scheme. By incorporating the datum of the rank of quadrics, a similar construction as the one in Chapter 2 yields new divisors in the moduli space of pointed curves. We compute the class of these divisors and show that the moduli space of 9-pointed genus 15 curves is a variety of general type. In Chapter 4, we present miscellaneous results, which are related with our main work in the previous chapters. Firstly, we consider divisors in the moduli space of genus g curves, which are defined as the failure locus of maximal rank conjecture for hypersurfaces of degree greater than two. We illustrate three examples of such divisors and compute their classes. Secondly, using the classical correspondence between rank 4 quadrics and pencils on curves, we show that the map that associates to a pair of pencils their tensor product in the Picard variety is surjective, when the curve is general and obvious numerical assumptions are satisfied. Finally, we use divisor classes, that are already known in the literature, to show that the moduli space of 10-pointed genus 12 curves is a variety of general type.

[pt] A produção de óleo e gás através de sistemas submarinos de produção vem sendo testada e realizada em diversos campos. As etapas iniciais do processamento primário, que eram realizadas nas Unidades Estacionárias de Produção (UEPs), vêm sendo deslocadas para o leito marinho, reduzindo os problemas de garantia de escoamento e aumentando a área disponível nas UEPs para processamento do óleo. Em primeiro lugar, o presente trabalho descreve os principais projetos de separação submarina já instalados e as motivações para suas aplicações. Adicionalmente, o presente trabalho apresenta os benefícios dos sistemas submarinos de separação água-óleo por meio dos resultados obtidos com um simulador de escoamento multifásico elaborado ao longo desta dissertação. Baseado no método de Beggs e Brill, este simulador foi desenvolvido na base computacional do Matlab e é capaz de avaliar a perda de carga no escoamento multifásico da produção em diversos arranjos submarinos. Por meio do simulador, foram feitas análises de sensibilidade para avaliar os efeitos das alterações nos principais parâmetros que influenciam o escoamento: razão água-óleo, razão gás-óleo, vazão de produção e grau API. Ao final do trabalho, são apresentados os cálculos das perdas de carga de dois arranjos submarinos hipotéticos que apresentam desafios relacionados à garantia de escoamento e a solução destes problemas com a instalação de sistemas submarinos de separação água-óleo. / [en] The production of oil and gas by subsea production systems has been tested and performed for several fields. The first steps of the primary oil and gas processing, which were held in Stationary Production Units (SPU), have been shifted to the seabed, reducing flow assurance problems and increasing the available area in SPUs for oil processing. On top to describing the main subsea separation projects and the reasons for their applications, the objective of this work is to present the benefits of subsea oil-water separation systems by means the results obtained with a multiphase flow simulator developed along this masters dissertation. Based on the method of Beggs and Brill, this simulator has been developed on Matlab platform and is able to evaluate the pressure drop of multiphase flows in various subsea production arrangements. With the simulator, a number of sensitivity analyzes is performed by changing the main parameters that affect the flow pressure drop: water-oil ratio, gas-oil ratio, production flow rate and API gravity. At the end of this work, the simulation results of two hypothetical subsea scenarios that have flow assurance problems and the solution of these problems with the installation of oil-water subsea separation systems are presented.

Ziel dieser Arbeit ist die explizite Berechnung gewisser geometrischer Zykel in Modulräumen von Kurven. In den letzten Jahren wurden Divisoren auf $\Mbar_{g,n}$ ausgiebig untersucht. Durch die Berechnung von Klassen in Kodimension 1 konnten wichtige Ergebnisse in der birationalen Geometrie der Räume $\Mbar_{g,n}$ erzielt werden. In Kapitel 1 geben wir einen Überblick über dieses Thema. Im Gegensatz dazu sind Klassen in Kodimension 2 im Großen und Ganzen unerforscht. In Kapitel 2 betrachten wir den Ort, der im Modulraum der Kurven vom Geschlecht 2k durch die Kurven mit einem Büschel vom Grad k definiert wird. Da die Brill-Noether-Zahl hier -2 ist, hat ein solcher Ort die Kodimension 2. Mittels der Methode der Testflächen berechnen wir die Klasse seines Abschlusses im Modulraum der stabilen Kurven. Das Ziel von Kapitel 3 ist es, die Klasse des Abschlusses des effektiven Divisors in $\Mbar_{6,1}$ zu berechnen, der durch punktierte Kurven [C, p] gegeben ist, für die ein ebenes Modell vom Grad 6 existiert, bei dem p auf einen Doppelpunkt abgebildet wird. Wie Jensen gezeigt hat, erzeugt dieser Divisor einen extremalen Strahl im pseudoeffektiven Kegel von $\Mbar_{6,1}$. Ein allgemeines Ergebnis über gewisse Familien von Linearsystemen mit angepasster Brill-Noether-Zahl 0 oder -1 wird eingeführt, um die Berechnung zu vervollständigen. / The aim of this thesis is the explicit computation of certain geometric cycles in moduli spaces of curves. In recent years, divisors of $\Mbar_{g,n}$ have been extensively studied. Computing classes in codimension one has yielded important results on the birational geometry of the spaces $\Mbar_{g,n}$. We give an overview of the subject in Chapter 1. On the contrary, classes in codimension two are basically unexplored. In Chapter 2 we consider the locus in the moduli space of curves of genus 2k defined by curves with a pencil of degree k. Since the Brill-Noether number is equal to -2, such a locus has codimension two. Using the method of test surfaces, we compute the class of its closure in the moduli space of stable curves. The aim of Chapter 3 is to compute the class of the closure of the effective divisor in $\M_{6,1}$ given by pointed curves [C,p] with a sextic plane model mapping p to a double point. Such a divisor generates an extremal ray in the pseudoeffective cone of $\Mbar_{6,1}$ as shown by Jensen. A general result on some families of linear series with adjusted Brill-Noether number 0 or -1 is introduced to complete the computation.