385 research outputs found
Coassociative submanifolds and G2-instantons in Joyce’s generalised Kummer constructions
No full textIn dieser Dissertation konstruieren wir neue Beispiele von koassoziativen Untermannigfaltigkeiten und G2-Instantonen in kompakten G2-Mannigfaltigkeiten, die aus Joyces verallgemeinerter Kummer Konstruktion hervorgehen. Die besondere Eigenschaft der in dieser Arbeit gefundenen koassoziativen Untermannigfaltigkeiten ist, dass ihr (topologisch bestimmtes) Volumen gegen Null geht, wenn die umgebende Mannigfaltigkeit sich ihrem Orbifaltigkeits-Limes annähert. Dies ist im Sinne eines Vorschlags von Halverson und Morrison, der darauf hinweist, dass bestimmte Entartungen (oder, allgemeiner, die Perioden) von G2-Strukturen durch das Verhalten von G2-topologischen Größen wie dem Volumen von assoziativen und koassoziativen Untermannigfaltigkeiten nachweisbar sein könnten.
Die Konstruktion dieser koassoziativen Untermannigfaltigkeiten ist Inhalt von Kapitel 3 und basiert auf der Deformation von „Modell-Untermannigfaltigkeiten“. Diese Untermannigfaltigkeiten liegen innerhalb des kritischen Bereiches der umgebenden Mannigfaltigkeit, in welchem die Metrik entartet. Abschnitt 3.3 beinhaltet zahlreiche Beispiele von koassoziativen Untermannigfaltigkeiten, die wir durch diese Methode konstruieren. Des Weiteren beschreiben wir die Deformationsfamilie dieser koassoziativen Untermannigfaltigkeiten.
In Kapitel 4 konstruieren wir neue Beispiele von G2-Instantonen über verallgemeinerten Kummer Konstruktionen. Wir konzentrieren uns hierbei hauptsächlich auf Auflösungen von Orbifaltigkeiten, deren singuläre Strata von Kodimension 6 sind. Wie im vorherigen Kapitel basiert die Konstruktion dieser Instantonen auf einem Klebesatz, welcher einen Zusammenhang deformiert, der (im quantifizierten Sinne) fast ein G2-Instanton ist. Außerdem benutzen wir Gruppenwirkungen um die Obstruktionen zu reduzieren. Mithilfe dieser Methode konstruieren wir in Abschnitt 4.4 eine unendliche Familie von G2-Instantonen auf einem Bündel über einer bestimmten Kummer Konstruktion.In this thesis we construct new examples of coassociative submanifolds and G2-instantons in compact G2-manifolds arising from Joyce’s generalised Kummer construction. The special feature of the coassociative submanifolds found in this thesis is that their (topologically determined) volume shrinks to zero as the ambient manifold approaches its orbifold limit. This is in the spirit of a proposal by Halverson and Morrison which indicates that certain degenerations (or, more general, the periods) of G2-structures may be detectable by the behaviour of G2-topological quantities such as the volume of associative and coassociative submanifolds.
The construction of these coassociative submanifolds is the content of Chapter 3. It is based on the deformation of ‘model-submanfiolds’. These submanifolds lie within the critical locus of the ambient manifold in which the metric degenerates. Section 3.3 contains numerous examples of coassociative submanifolds which we construct via this method. Furthermore, we give a description of the deformation family of these coassociative submanifolds.
In Chapter 4 we construct new examples of G2-instantons over generalised Kummer constructions. We focus mainly on resolutions of orbifolds whose singular strata are of codimension 6. As in the previous chapter, the construction of these instantons is based on a gluing theorem which deforms a connection that is (in a quantified sense) close to being a G2-instanton. Furthermore, we use group actions to reduce the obstructions. Using this method, we construct in Section 4.4 an infinite family of G2-instantons on a bundle over one particular Kummer construction
Three problems related to the Kummer problem
No full textНаведено короткий огляд основних результатів з індивідуальної проблеми Куммера, а також нові результати автора з цієї проблеми.We give a brief survey of the principal results concerning the individual Kummer problem and present new results of the author concerning this problem
On a theorem of Kummer
No full textAbstractThe author gives a simple proof of a theorem of Kummer. Let q denote an odd prime, e = (q − 1)2 and let fe(x) denote the polynomial with leading coefficient 1 whose roots are 2 cos (2mπq) with 1 ≤ m ≤ e. Then all prime divisors p of the polynomial fe(x) have the form p ≡ ± 1 (rmmod q), except for p = q
Friedrich August Kummer and his works for two cellos
No full textThis master thesis deal with the cellist Friedrich August Kummer a representative of the Dresden school and his works for two cellos. Parts of the thesis are: informations about cello music in Germany, representatives of the Dresden school, Kummer´s biography and Method, description of some works for two cellos and analysis of selected movements of his 3 cello duets op.22. The author colected information from websites, books and sheet music
ALGEBRAIC CHAMPS AND KUMMER COVERINGS
No full textIn this article, the author studies the conditions such that special stacks are algebraic and proves that Kummer coverings form algebraic stacks ([La2]). The notion of K. Kato's logarithmic spaces ([Ka]) is enlarged to work in the category of algebraic stacks. By virtue of these notions, he constructs an endomorphism assumed in Kahler analogue of certain conjectures of Weil ([Ser]) by Serre.3KJ00001512026論文Articledepartmental bulletin pape
Explicit Serre weights for GL_2 via Kummer theory
No full textWe give an explicit formulation of the weight part of Serre's conjecture for GL_2 using Kummer theory. This avoids any reference to p-adic Hodge theory. The key inputs are a description of the reduction modulo p of crystalline extensions in terms of certain "G_K-Artin-Scheier cocycles" and a result of Abrashkin which describes these cocycles in terms of Kummer theory. An alternative explicit formulation in terms of local class field theory was previously given by Dembele-Diamond-Roberts in the unramified case and by the second author in general. We show that the description of Dembele-Diamond-Roberts can be recovered directly from ours using the explicit reciprocity laws of Brueckner-Shaferevich-Vostokov. These calculations illustrate how our use of Kummer theory eliminates certain combinatorial complications appearing in these two papers
Division in modules and Kummer theory
No full textIn this work we generalize the concept of injective module and develop a theory of divisibility for modules over a general ring, which provides a general and unified framework to study Kummer-like field extensions arising from commutative algebraic groups. With these tools we provide an effective bound for the degree of the field extensions arising from division points of elliptic curves, extending previous results of Javan Peykar for CM curves and of Lombardo and the author for the non-CM case
Let’s collaborate, but I will be the first author! Exploring the importance of the first authorship for IS researchers
No full textCollaboration among researchers is typically seen as the quintessence of academic excellence, leading to improvements in the research quality, capitalization on the diversity of perspectives and gains in productivity. Despite these benefits, many research teams find themselves torn by competition,
antagonism and resentment. Desire to be the first author and resultant underperformance of non-first co-authors is often at the root of these conflicts. At the same time little is known about what motivates
researchers in general and IS researchers in particular to engage as first authors. To fill this gap, this study uses survey methodology to explore the attitudes of IS researchers and their resulting behavior when it comes to authors order. Qualitative and quantitative evidence collected from 398 IS
researchers is used to support our analysis. We find that researchers’ desire to be the first authors is mainly driven by such determinants as career aspirations, visibility, leadership and sense of ownership, and less so by the desire to satisfy their self-esteem and self-actualization needs. In
addition, the value placed on being the first author appears to be the function of researchers’ career level, with Ph.D. students attaching significantly higher value to it than senior scholars
Global dynamics of the Kummer-Schwarz differential equation
No full textAgraïments: The second author is partially supported by Dirección de Investigación DIUBB 1204084/RThis paper studies the Kummer-Schwarz differential equation 2 ˙x...x −3¨x2 = 0 which is of special interest due to its relationship with the Schwarzian derivative. This differential equation is transformed into a first order differential system in R3, and we provide a complete description of its global dynamics adding the infinity
Global dynamics of the Kummer-Schwarz differential equation
No full textAgraïments: The second author is partially supported by Dirección de Investigación DIUBB 1204084/RThis paper studies the Kummer-Schwarz differential equation 2 ˙x...x -3¨x2 = 0 which is of special interest due to its relationship with the Schwarzian derivative. This differential equation is transformed into a first order differential system in R3, and we provide a complete description of its global dynamics adding the infinity
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