Search Results for "sheaf-theory-graduate-texts-in-mathematics"

Sheaf Theory

Sheaf Theory

  • Author: Glen E. Bredon
  • Publisher: Springer Science & Business Media
  • ISBN: 1461206472
  • Category: Mathematics
  • Page: 504
  • View: 1125
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Primarily concerned with the study of cohomology theories of general topological spaces with "general coefficient systems", the parts of sheaf theory covered here are those areas important to algebraic topology. Among the many innovations in this book, the concept of the "tautness" of a subspace is introduced and exploited; the fact that sheaf theoretic cohomology satisfies the homotopy property is proved for general topological spaces; and relative cohomology is introduced into sheaf theory. A list of exercises at the end of each chapter helps students to learn the material, and solutions to many of the exercises are given in an appendix. This new edition of a classic has been substantially rewritten and now includes some 80 additional examples and further explanatory material, as well as new sections on Cech cohomology, the Oliver transfer, intersection theory, generalised manifolds, locally homogeneous spaces, homological fibrations and p- adic transformation groups. Readers should have a thorough background in elementary homological algebra and in algebraic topology.

Numerische Behandlung partieller Differentialgleichungen

Numerische Behandlung partieller Differentialgleichungen

  • Author: Christian Großmann,Hans-Görg Roos
  • Publisher: Springer-Verlag
  • ISBN: 9783519220893
  • Category: Mathematics
  • Page: 572
  • View: 3300
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Mathematiker, Naturwissenschaftler und Ingenieure erhalten mit diesem Lehrbuch eine Einführung in die numerische Behandlung partieller Differentialgleichungen. Diskutiert werden die grundlegenden Verfahren - Finite Differenzen, Finite Volumen und Finite Elemente - für die wesentlichen Typen partieller Differentialgleichungen: elliptische, parabolische und hyperbolische Gleichungen. Einbezogen werden auch moderne Methoden zur Lösung der diskreten Probleme. Hinweise auf aktuelle Software sowie zahlreiche Beispiele und Übungsaufgaben runden diese Einführung ab.

Zahlen

Zahlen

  • Author: Heinz-Dieter Ebbinghaus,Hans Hermes,Friedrich Hirzebruch,Max Koecher,Klaus Mainzer,Jürgen Neukirch,Alexander Prestel,Reinhold Remmert
  • Publisher: Springer-Verlag
  • ISBN: 3642971229
  • Category: Mathematics
  • Page: 337
  • View: 1219
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Aus den Besprechungen: "Ein Mathematikbuch der Superlativen, für Mathematiker (jeder Schattierung) und Nichtmathematiker (denen völlig unbekannte Dimensionen der Mathematik eröffnet werden - künstlerische, magische, historische, philosophische, wissenschaftstheoretische, "unlogische", phantasieerfüllte usw.). Der Aufbau ist meisterhaft, die Lektüre höchst anregend und leicht lesbar." Monatshefte für Mathematik #1 "Ein gelungenes Werk, das dem Vorurteil entgegenwirkt, Mathematik bestehe nur aus isolierten Theorien." Die NEUE HOCHSCHULE #1 "Das Lesen ist ein Genuß, den man sich nicht entgehen lassen sollte." Jahresbericht der Deutschen Mathematiker-Vereinigung #1

Sheaf Theory

Sheaf Theory

  • Author: B. R. Tennison
  • Publisher: Cambridge University Press
  • ISBN: 0521207843
  • Category: Mathematics
  • Page: 164
  • View: 6843
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Sheaf theory provides a means of discussing many different kinds of geometric objects in respect of the connection between their local and global properties. It finds its main applications in topology and modern algebraic geometry where it has been used as a tool for solving, with great success, several long-standing problems. This text is based on a lecture course for graduate pure mathematicians which builds up enough of the foundations of sheaf theory to give a broad definition of manifold, covering as special cases the algebraic geometer's schemes as well as the topological, differentiable and analytic kinds, and to define sheaf cohomology for application to such objects. Exercises are provided at the end of each chapter and at various places in the text. Hints and solutions to some of them are given at the end of the book.

Lineare Darstellungen endlicher Gruppen

Lineare Darstellungen endlicher Gruppen

  • Author: Jean Pierre Serre
  • Publisher: Springer-Verlag
  • ISBN: 3322858634
  • Category: Mathematics
  • Page: 102
  • View: 1676
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Neue Topologische Methoden in der Algebraischen Geometrie

Neue Topologische Methoden in der Algebraischen Geometrie

  • Author: Friedrich Hirzebruch
  • Publisher: Springer-Verlag
  • ISBN: 3662410834
  • Category: Mathematics
  • Page: 165
  • View: 3690
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Several Complex Variables with Connections to Algebraic Geometry and Lie Groups

Several Complex Variables with Connections to Algebraic Geometry and Lie Groups

  • Author: Joseph L. Taylor
  • Publisher: American Mathematical Soc.
  • ISBN: 082183178X
  • Category: Mathematics
  • Page: 507
  • View: 678
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This text presents an integrated development of the theory of several complex variables and complex algebraic geometry, leading to proofs of Serre's celebrated GAGA theorems relating the two subjects, and including applications to the representation theory of complex semisimple Lie groups. It includes a thorough treatment of the local theory using the tools of commutative algebra, an extensive development of sheaf theory and the theory of coherent analytic and algebraic sheaves, proofs of the main vanishing theorems for these categories of sheaves, and a complete proof of the finite dimensionality of the cohomology of coherent sheaves on compact varieties. The vanishing theorems have a wide variety of applications and these are covered in detail. Of particular interest are the last three chapters, which are devoted to applications of the preceding material to the study of the structure and representations of complex semisimple Lie groups.Included in this text are introductions to harmonic analysis, the Peter-Weyl theorem, Lie theory and the structure of Lie algebras, semisimple Lie algebras and their representations, algebraic groups and the structure of complex semisimple Lie groups. All of this culminates in Milicic's proof of the Borel-Weil-Bott theorem, which makes extensive use of the material developed earlier in the text. There are numerous examples and exercises in each chapter. This modern treatment of a classic point of view would be an excellent text for a graduate course on several complex variables, as well as a useful reference for the expert.

Advances in Theoretical and Mathematical Physics

Advances in Theoretical and Mathematical Physics

ATMP.

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematical physics
  • Page: N.A
  • View: 8567
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The Geometry of Moduli Spaces of Sheaves

The Geometry of Moduli Spaces of Sheaves

A Publication of the Max-Planck-Institut für Mathematik, Bonn

  • Author: Daniel Huybrechts,Manfred Lehn
  • Publisher: Vieweg+Teubner Verlag
  • ISBN: 9783663116257
  • Category: Technology & Engineering
  • Page: 270
  • View: 4145
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This book is intended to serve as an introduction to the theory of semistable sheaves and at the same time to provide a survey of recent research results on the geometry of moduli spaces. The first part introduces the basic concepts in the theory: Hilbert polynomial, slope, stability, Harder-Narasimhan filtration, Grothendieck's Quot-scheme. It presents detailed proofs of the Grauert-Mülich Theorem, the Bogomolov Inequality, the semistability of tensor products, and the boundedness of the family of semistable sheaves. It also gives a self-contained account of the construction of moduli spaces of semistable sheaves on a projective variety à la Gieseker, Maruyama, and Simpson. The second part presents some of the recent results of the geometry of moduli spaces of sheaves on an algebraic surface, following work of Mukai, O'Grady, Gieseker, Li and many others. In particular, moduli spaces of sheaves on K3 surfaces and determinant line bundles on the moduli spaces are treated in some detail. Other topics include the Serre correspondence, restriction of stable bundles to curves, symplectic structures, irreducibility and Kodaira-dimension of moduli spaces.

Geometric Analysis and Lie Theory in Mathematics and Physics

Geometric Analysis and Lie Theory in Mathematics and Physics

  • Author: Alan L. Carey,Michael K. Murray,J. H. Loxton
  • Publisher: Cambridge University Press
  • ISBN: 9780521624909
  • Category: Mathematics
  • Page: 290
  • View: 7756
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Graduate lectures on the interface between mathematics and physics.

Using the Mathematics Literature

Using the Mathematics Literature

  • Author: Kristine K. Fowler
  • Publisher: CRC Press
  • ISBN: 9780824750350
  • Category: Language Arts & Disciplines
  • Page: 475
  • View: 473
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This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.

An Introduction to Partially Ordered Structures and Sheaves

An Introduction to Partially Ordered Structures and Sheaves

  • Author: Francisco Miraglia
  • Publisher: Polimetrica s.a.s.
  • ISBN: 8876990356
  • Category: Mathematics
  • Page: 511
  • View: 1864
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Algebraic Geometry

Algebraic Geometry

  • Author: Masayoshi Miyanishi
  • Publisher: American Mathematical Soc.
  • ISBN: 9780821887707
  • Category: Mathematics
  • Page: 246
  • View: 5204
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Students often find, in setting out to study algebraic geometry, that most of the serious textbooks on the subject require knowledge of ring theory, field theory, local rings, and transcendental field extensions, and even sheaf theory. Often the expected background goes well beyond college mathematics. This book, aimed at senior undergraduates and graduate students, grew out of Miyanishi's attempt to lead students to an understanding of algebraic surfaces while presenting thenecessary background along the way. Originally published in Japanese in 1990, it presents a self-contained introduction to the fundamentals of algebraic geometry. This book begins with background on commutative algebras, sheaf theory, and related cohomology theory. The next part introduces schemes andalgebraic varieties, the basic language of algebraic geometry. The last section brings readers to a point at which they can start to learn about the classification of algebraic surfaces.

Principia Mathematica.

Principia Mathematica.

  • Author: Alfred North Whitehead,Bertrand Russell
  • Publisher: N.A
  • ISBN: N.A
  • Category: Logic, Symbolic and mathematical
  • Page: 167
  • View: 4058
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Gewöhnliche Differentialgleichungen

Gewöhnliche Differentialgleichungen

Eine Einführung

  • Author: Wolfgang Walter
  • Publisher: Springer-Verlag
  • ISBN: 364296317X
  • Category: Mathematics
  • Page: 232
  • View: 4454
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An Introduction to Intersection Homology Theory, Second Edition

An Introduction to Intersection Homology Theory, Second Edition

  • Author: Frances Kirwan,Jonathan Woolf
  • Publisher: CRC Press
  • ISBN: 9781584881841
  • Category: Mathematics
  • Page: 248
  • View: 966
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Now more that a quarter of a century old, intersection homology theory has proven to be a powerful tool in the study of the topology of singular spaces, with deep links to many other areas of mathematics, including combinatorics, differential equations, group representations, and number theory. Like its predecessor, An Introduction to Intersection Homology Theory, Second Edition introduces the power and beauty of intersection homology, explaining the main ideas and omitting, or merely sketching, the difficult proofs. It treats both the basics of the subject and a wide range of applications, providing lucid overviews of highly technical areas that make the subject accessible and prepare readers for more advanced work in the area. This second edition contains entirely new chapters introducing the theory of Witt spaces, perverse sheaves, and the combinatorial intersection cohomology of fans. Intersection homology is a large and growing subject that touches on many aspects of topology, geometry, and algebra. With its clear explanations of the main ideas, this book builds the confidence needed to tackle more specialist, technical texts and provides a framework within which to place them.

Elementare Algebraische Geometrie

Elementare Algebraische Geometrie

Grundlegende Begriffe und Techniken mit zahlreichen Beispielen und Anwendungen

  • Author: Klaus Hulek
  • Publisher: Springer-Verlag
  • ISBN: 3322802213
  • Category: Mathematics
  • Page: 167
  • View: 3898
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Dieses Buch gibt eine Einführung in die Algebraische Geometrie. Ziel ist es, die grundlegenden Begriffe und Techniken der algebraischen Geometrie zusammen mit einer Reihe von Beispielen darzustellen.

Vorlesungen über die Theorie der algebraischen Zahlen

Vorlesungen über die Theorie der algebraischen Zahlen

  • Author: Erich Hecke
  • Publisher: University of Pennsylvania Press
  • ISBN: 9780821821435
  • Category: Mathematics
  • Page: 274
  • View: 3264
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This title has been described as An elegant and comprehensive account of the modern theory of algebraic numbers - Bulletin of the AMS.

Grundkurs Topologie

Grundkurs Topologie

  • Author: Gerd Laures,Markus Szymik
  • Publisher: Springer-Verlag
  • ISBN: 3827422183
  • Category: Mathematics
  • Page: 242
  • View: 7688
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Die Topologie beschäftigt sich mit den qualitativen Eigenschaften geometrischer Objekte. Ihr Begriffsapparat ist so mächtig, dass kaum eine mathematische Struktur nicht mit Gewinn topologisiert wurde. Dieses Buch versteht sich als Brücke von den einführenden Vorlesungen der Analysis und Linearen Algebra zu den fortgeschrittenen Vorlesungen der Algebraischen und Geometrischen Topologie. Es eignet sich besonders für Studierende in einem Bachelor- oder Masterstudiengang der Mathematik, kann aber auch zum Selbststudium für mathematisch interessierte Naturwissenschaftler dienen. Die Autoren legen besonderen Wert auf eine moderne Sprache, welche die vorgestellten Ideen vereinheitlicht und damit erleichtert. Definitionen werden stets mit vielen Beispielen unterlegt und neue Konzepte werden mit zahlreichen Bildern illustriert. Über 170 Übungsaufgaben (mit Lösungen zu ausgewählten Aufgaben auf der Website zum Buch) helfen, die vermittelten Inhalte einzuüben und zu vertiefen. Viele Abschnitte werden ergänzt durch kurze Einblicke in weiterführende Themen, die einen Ausgangspunkt für Studienarbeiten oder Seminarthemen bieten. Neben dem üblichen Stoff zur mengentheoretischen Topologie, der Theorie der Fundamentalgruppen und der Überlagerungen werden auch Bündel, Garben und simpliziale Methoden angesprochen, welche heute zu den Grundbegriffen der Geometrie und Topologie gehören.

Lineare Operatoren in Hilberträumen

Lineare Operatoren in Hilberträumen

Teil 1 Grundlagen

  • Author: Joachim Weidmann
  • Publisher: Springer-Verlag
  • ISBN: 9783322800947
  • Category: Mathematics
  • Page: 475
  • View: 7201
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Behandelt werden die Grundlagen der Theorie zum Thema Lineare Operatoren in Hilberträumen, wie sie üblicherweise in Standardvorlesungen für Mathematiker und Physiker vorgestellt werden.