Algebraic Spaces and Stacks

Author: Martin Olsson

Publisher: American Mathematical Soc.

ISBN: 1470427982

Category: Algebraic spaces

Page: 298

View: 1077

This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix.
Release

Algebraic Spaces and Stacks

Author: Martin Olsson

Publisher: American Mathematical Soc.

ISBN: 1470427982

Category: Algebraic spaces

Page: 298

View: 1420

This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix.
Release

Moduli of Curves

CIMAT Guanajuato, Mexico 2016

Author: Leticia Brambila Paz,Ciro Ciliberto,Eduardo Esteves,Margarida Melo,Claire Voisin

Publisher: Springer

ISBN: 3319594869

Category: Mathematics

Page: 242

View: 569

Providing a timely description of the present state of the art of moduli spaces of curves and their geometry, this volume is written in a way which will make it extremely useful both for young people who want to approach this important field, and also for established researchers, who will find references, problems, original expositions, new viewpoints, etc. The book collects the lecture notes of a number of leading algebraic geometers and in particular specialists in the field of moduli spaces of curves and their geometry. This is an important subject in algebraic geometry and complex analysis which has seen spectacular developments in recent decades, with important applications to other parts of mathematics such as birational geometry and enumerative geometry, and to other sciences, including physics. The themes treated are classical but with a constant look to modern developments (see Cascini, Debarre, Farkas, and Sernesi's contributions), and include very new material, such as Bridgeland stability (see Macri's lecture notes) and tropical geometry (see Chan's lecture notes).
Release

Rational Points on Varieties

Author: Bjorn Poonen

Publisher: American Mathematical Soc.

ISBN: 1470437732

Category: Algebraic varieties

Page: 337

View: 6216

This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere.
Release

Geometry of Algebraic Curves

Volume II with a contribution by Joseph Daniel Harris

Author: Enrico Arbarello,Maurizio Cornalba,Phillip Griffiths

Publisher: Springer Science & Business Media

ISBN: 9783540693925

Category: Mathematics

Page: 963

View: 4938

The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface with the theoretical physics community. The approach is unique in its blending of algebro-geometric, complex analytic and topological/combinatorial methods. It treats important topics such as Teichmüller theory, the cellular decomposition of moduli and its consequences and the Witten conjecture. The careful and comprehensive presentation of the material is of value to students who wish to learn the subject and to experts as a reference source. The first volume appeared 1985 as vol. 267 of the same series.
Release

Differentialgeometrie, Topologie und Physik

Author: Mikio Nakahara

Publisher: Springer-Verlag

ISBN: 3662453002

Category: Science

Page: 597

View: 3866

Differentialgeometrie und Topologie sind wichtige Werkzeuge für die Theoretische Physik. Insbesondere finden sie Anwendung in den Gebieten der Astrophysik, der Teilchen- und Festkörperphysik. Das vorliegende beliebte Buch, das nun erstmals ins Deutsche übersetzt wurde, ist eine ideale Einführung für Masterstudenten und Forscher im Bereich der theoretischen und mathematischen Physik. - Im ersten Kapitel bietet das Buch einen Überblick über die Pfadintegralmethode und Eichtheorien. - Kapitel 2 beschäftigt sich mit den mathematischen Grundlagen von Abbildungen, Vektorräumen und der Topologie. - Die folgenden Kapitel beschäftigen sich mit fortgeschritteneren Konzepten der Geometrie und Topologie und diskutieren auch deren Anwendungen im Bereich der Flüssigkristalle, bei suprafluidem Helium, in der ART und der bosonischen Stringtheorie. - Daran anschließend findet eine Zusammenführung von Geometrie und Topologie statt: es geht um Faserbündel, characteristische Klassen und Indextheoreme (u.a. in Anwendung auf die supersymmetrische Quantenmechanik). - Die letzten beiden Kapitel widmen sich der spannendsten Anwendung von Geometrie und Topologie in der modernen Physik, nämlich den Eichfeldtheorien und der Analyse der Polakov'schen bosonischen Stringtheorie aus einer gemetrischen Perspektive. Mikio Nakahara studierte an der Universität Kyoto und am King’s in London Physik sowie klassische und Quantengravitationstheorie. Heute ist er Physikprofessor an der Kinki-Universität in Osaka (Japan), wo er u. a. über topologische Quantencomputer forscht. Diese Buch entstand aus einer Vorlesung, die er während Forschungsaufenthalten an der University of Sussex und an der Helsinki University of Sussex gehalten hat.
Release

Codierungstheorie

Konstruktion und Anwendung linearer Codes

Author: Anton Betten,Harald Fripertinger,Adalbert Kerber,Alfred Wassermann,Karl-Heinz Zimmermann

Publisher: Springer-Verlag

ISBN: 3642589731

Category: Computers

Page: 338

View: 7252

Diese Einführung in die Theorie der linearen Codes behandelt besonders ausführlich zyklische Codes. Daneben liegt ein Schwerpunkt auf computerunterstützten Methoden, insbesondere für die Bestimmung der Minimaldistanz linearer Codes, für die Abzählung der Isometrieklassen linearer Codes sowie Blockcodes und für die Erzeugung von Repräsentantensystemen dieser Klassen.
Release

Anschauliche Geometrie

Author: David Hilbert,Stefan Cohn-Vossen

Publisher: Springer-Verlag

ISBN: 3662366851

Category: Mathematics

Page: 312

View: 2003

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.
Release

Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces

Author: I͡U. I. Manin,Yuri I. Manin,︠I︡U. I. Manin,隝霼. I.·Manin,Kilu I Manin

Publisher: American Mathematical Soc.

ISBN: 0821819178

Category: Mathematics

Page: 303

View: 8147

The author was once the director of the Max-Planck-Institut fur Mathematik in Bonn, Germany, one of the most prestigious mathematics institutions in the world. Topic expands into the realm of physics, and can be placed in a physics section. The Colloquium series offers classics in the mathematical literature, and can be favorably compared to books now being published in the AMS Chelsea series.
Release

Distributionen Und Hilbertraumoperatoren

Mathematische Methoden Der Physik

Author: Philippe Blanchard,Erwin Brüning

Publisher: Springer

ISBN: 9783211825075

Category: Science

Page: 375

View: 8105

Das Buch bietet eine Einführung in die zum Studium der Theoretischen Physik notwendigen mathematischen Grundlagen. Der erste Teil des Buches beschäftigt sich mit der Theorie der Distributionen und vermittelt daneben einige Grundbegriffe der linearen Funktionalanalysis. Der zweite Teil baut darauf auf und gibt eine auf das Wesentliche beschränkte Einführung in die Theorie der linearen Operatoren in Hilbert-Räumen. Beide Teile werden von je einer Übersicht begleitet, die die zentralen Ideen und Begriffe knapp erläutert und den Inhalt kurz beschreibt. In den Anhängen werden einige grundlegende Konstruktionen und Konzepte der Funktionalanalysis dargestellt und wichtige Konsequenzen entwickelt.
Release

Arithmetic and Geometry Around Quantization

Author: Özgür Ceyhan,Yu. I. Manin,Matilde Marcolli

Publisher: Springer Science & Business Media

ISBN: 0817648313

Category: Mathematics

Page: 292

View: 8623

This volume comprises both research and survey articles originating from the conference on Arithmetic and Geometry around Quantization held in Istanbul in 2006. A wide range of topics related to quantization are covered, thus aiming to give a glimpse of a broad subject in very different perspectives.
Release

Gesammelte Abhandlungen III

Author: Carl Ludwig Siegel

Publisher: Springer

ISBN: 9783540093749

Category: Mathematics

Page: 484

View: 2475

From the Preface by K. Chandrasekharan: "The publication of this collection of papers is intended as a service to the mathematical community, as well as a tribute to the genius of CARL LUDWIG SIEGEL. In the wide range of his interests, in his capacity to uncover, to attack, and to subdue problems of great significance and difficulty, in his invention of new concepts and ideas, in his technical prowess, and in the consummate artistry of his presentation, SIEGEL resembles the classical figures of mathematics. In his combination of arithmetical, analytical, algebraical, and geometrical methods of investigation, and in his unerring instinct for the conceptual and structural, as distinct from the merely technical, aspects of any concrete problem, he represents the best type of modern mathematical thought. At once classical and modern, his work has profoundly influenced the mathematical culture of our time... this publication...will no doubt stimulate generations of scholars to come." Volume III collects Siegel ́s papers from 1945 to 1964.
Release

Geschichte eines Deutschen

Die Erinnerungen 1914-1933

Author: Sebastian Haffner

Publisher: DVA

ISBN: 3641155533

Category: Biography & Autobiography

Page: 304

View: 9116

Ein einzigartiges Zeitzeugnis Als Kind und junger Mann erlebte Sebastian Haffner den Ersten Weltkrieg, die galoppierende Inflation 1923, die Radikalisierung der politischen Parteien, den unaufhaltsamen Aufstieg der Nationalsozialisten. Ohne politisch oder rassisch verfolgt zu sein, emigrierte er 1938. Aus dem Nachlass wurden diese Erinnerungen seiner ersten drei Lebensjahrzehnte veröffentlicht, die Haffner 1939 in England zu Papier gebracht hatte. Um zwei neu aufgefundene Manuskriptteile erweiterte Ausgabe.
Release

Lehrbuch Der Algebra

Author: Heinrich Weber

Publisher: American Mathematical Soc.

ISBN: 0821832581

Category: Mathematics

Page: 703

View: 7267

Weber's three-volume set on algebra was for many years the standard text on algebra. Published at the end of the nineteenth century, it helped usher group theory to a central place in twentieth century mathematics. Volume 1 covers foundational material. Volume 2 covers group theory and its applications, plus the theory of algebraic numbers. Volume 3 covers advanced topics, such as algebraic functions, elliptic functions and class field theory. Although notations have changed somewhat and algebra has become more abstract that it was in Weber's day, many of the same themes and ideas important today are central topics in Weber's book, which may be why it has become a classic.
Release

Vorlesungen über die Theorie der algebraischen Zahlen

Author: Erich Hecke

Publisher: University of Pennsylvania Press

ISBN: 9780821821435

Category: Mathematics

Page: 274

View: 563

This title has been described as An elegant and comprehensive account of the modern theory of algebraic numbers - Bulletin of the AMS.
Release