Riemann Surfaces and Algebraic Curves

Author: Renzo Cavalieri
Publisher: Cambridge University Press
ISBN: 1316798933
Format: PDF
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Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.

Topological Recursion and its Influence in Analysis Geometry and Topology

Author: Chiu-Chu Melissa Liu
Publisher: American Mathematical Soc.
ISBN: 1470435411
Format: PDF
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This volume contains the proceedings of the 2016 AMS von Neumann Symposium on Topological Recursion and its Influence in Analysis, Geometry, and Topology, which was held from July 4–8, 2016, at the Hilton Charlotte University Place, Charlotte, North Carolina. The papers contained in the volume present a snapshot of rapid and rich developments in the emerging research field known as topological recursion. It has its origin around 2004 in random matrix theory and also in Mirzakhani's work on the volume of moduli spaces of hyperbolic surfaces. Topological recursion has played a fundamental role in connecting seemingly unrelated areas of mathematics such as matrix models, enumeration of Hurwitz numbers and Grothendieck's dessins d'enfants, Gromov-Witten invariants, the A-polynomials and colored polynomial invariants of knots, WKB analysis, and quantization of Hitchin moduli spaces. In addition to establishing these topics, the volume includes survey papers on the most recent key accomplishments: discovery of the unexpected relation to semi-simple cohomological field theories and a solution to the remodeling conjecture. It also provides a glimpse into the future research direction; for example, connections with the Airy structures, modular functors, Hurwitz-Frobenius manifolds, and ELSV-type formulas.

Cyclic Coverings Calabi Yau Manifolds and Complex Multiplication

Author: Christian Rohde
Publisher: Springer Science & Business Media
ISBN: 3642006388
Format: PDF, ePub
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The main goal of this book is the construction of families of Calabi-Yau 3-manifolds with dense sets of complex multiplication fibers. The new families are determined by combining and generalizing two methods. Firstly, the method of E. Viehweg and K. Zuo, who have constructed a deformation of the Fermat quintic with a dense set of CM fibers by a tower of cyclic coverings. Using this method, new families of K3 surfaces with dense sets of CM fibers and involutions are obtained. Secondly, the construction method of the Borcea-Voisin mirror family, which in the case of the author's examples yields families of Calabi-Yau 3-manifolds with dense sets of CM fibers, is also utilized. Moreover fibers with complex multiplication of these new families are also determined. This book was written for young mathematicians, physicists and also for experts who are interested in complex multiplication and varieties with complex multiplication. The reader is introduced to generic Mumford-Tate groups and Shimura data, which are among the main tools used here. The generic Mumford-Tate groups of families of cyclic covers of the projective line are computed for a broad range of examples.

Vorlesungen ber Das Ikosaeder Und Die Aufl sung Der Gleichungen Vom F nften Grade

Author: Felix Klein
Publisher: Wentworth Press
ISBN: 9780270562392
Format: PDF, ePub
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This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

An Evening of Long Goodbyes

Author: Paul Murray
Publisher: Antje Kunstmann
ISBN: 3888978335
Format: PDF, ePub
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Paul Murrays brillanter Gesellschaftsroman erzählt die Geschichte von Charles Hythloday, der im Herrenhaus seiner Familie den skurrilen Lebensstil eines Landedelmanns pflegt. Umsorgt von der bosnischen Haushälterin verbringt er seine Tage Cocktails schlürfend auf der Chaiselongue und schaut sich alte Schwarzweißfilme an. Als regelmäßige Arbeit sieht er die unregelmäßige Pflege der Pfauen seines verstorbenen Vaters. Allerdings müssen Charles und seine Schwester Bel bald feststellen, dass sie nicht so reich sind, wie sie dachten. Die von einem Alkoholentzug nach Hause zurückkehrende Mutter zwingt Charles, sich einen Job zu suchen, den Landsitz zu verlassen und endlich auf eigenen Beinen zu stehen. Doch auf die harte Realität in Dublin ist er nicht vorbereitet. Andererseits ist das wirkliche Leben aber auch nicht vorbereitet auf einen wie Charles Hythloday...

Ebene algebraische Kurven

Author: Gerd Fischer
Publisher: Springer-Verlag
ISBN: 3322803112
Format: PDF, ePub, Mobi
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Neben den elementaren Dingen, wie Tangenten, Singularitäten und Wendepunkten werden auch schwierigere Begriffe wie lokale Zweige und Geschlecht behandelt. Höhepunkte sind die klassischen Formeln von Plücker und Clebsch, die Beziehungen zwischen verschiedenen globalen und lokalen Invarianten einer Kurve beschreiben.

Vorlesungen ber die Zahlentheorie der Quaternionen

Author: Adolf Hurwitz
Publisher: Springer-Verlag
ISBN: 3642475361
Format: PDF, ePub, Docs
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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.