Einfuhrung In Die Kommutative Algebra Und Algebraische Geometrie

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Introduction to Commutative Algebra and Algebraic Geometry

Author : Ernst Kunz
Publisher : Springer Science & Business Media
ISBN 13 : 1461459877
Total Pages : 238 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Introduction to Commutative Algebra and Algebraic Geometry by : Ernst Kunz

Download or read book Introduction to Commutative Algebra and Algebraic Geometry written by Ernst Kunz and published by Springer Science & Business Media. This book was released on 2012-11-06 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.

Einführung in die kommutative Algebra und algebraische Geometrie

Author : Ernst Kunz
Publisher : Springer-Verlag
ISBN 13 : 3322855260
Total Pages : 252 pages
Book Rating : 4.3/5 (228 download)

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Book Synopsis Einführung in die kommutative Algebra und algebraische Geometrie by : Ernst Kunz

Download or read book Einführung in die kommutative Algebra und algebraische Geometrie written by Ernst Kunz and published by Springer-Verlag. This book was released on 2013-03-09 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Eine Einführung in die kommutative Algebra und algebraische Geometrie

Author : Ernst Kunz
Publisher :
ISBN 13 :
Total Pages : 345 pages
Book Rating : 4.:/5 (632 download)

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Book Synopsis Eine Einführung in die kommutative Algebra und algebraische Geometrie by : Ernst Kunz

Download or read book Eine Einführung in die kommutative Algebra und algebraische Geometrie written by Ernst Kunz and published by . This book was released on 1978 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Commutative Algebra and Algebraic Geometry

Author : Ernst Kunz
Publisher : Birkhäuser
ISBN 13 : 9781461252900
Total Pages : 0 pages
Book Rating : 4.2/5 (529 download)

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Book Synopsis Introduction to Commutative Algebra and Algebraic Geometry by : Ernst Kunz

Download or read book Introduction to Commutative Algebra and Algebraic Geometry written by Ernst Kunz and published by Birkhäuser. This book was released on 1984 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been estimated that, at the present stage of our knowledge, one could give a 200 semester course on commutative algebra and algebraic geometry without ever repeating himself. So any introduction to this subject must be highly selective. I first want to indicate what point of view guided the selection of material for this book. This introduction arose from lectures for students who had taken a basic course in algebra and could therefore be presumed to have a knowledge of linear algebra, ring and field theory, and Galois theory. The present text shouldn't require much more. In the lectures and in this text I have undertaken with the fewest possible auxiliary means to lead up to some recent results of commutative algebra and algebraic geometry concerning the representation of algebraic varieties as in tersections of the least possible number of hypersurfaces and- a closely related problem-with the most economical generation of ideals in Noetherian rings. The question of the equations needed to describe an algebraic variety was addressed by Kronecker in 1882. In the 1940s it was chiefly Perron who was interested in this question; his discussions with Severi made the problem known and contributed to sharpening the rei event concepts. Thanks to the general progress of commutative algebra many beautiful results in this circle of questions have been obtained, mainly after the solution of Serre's problem on projective modules. Because of their relatively elementary character they are especially suitable for an introduction to commutative algebra.

Kommutative Algebra und Algebraische Geometrie

Author : Jürgen Böhm
Publisher : Springer-Verlag
ISBN 13 : 366259482X
Total Pages : 537 pages
Book Rating : 4.6/5 (625 download)

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Book Synopsis Kommutative Algebra und Algebraische Geometrie by : Jürgen Böhm

Download or read book Kommutative Algebra und Algebraische Geometrie written by Jürgen Böhm and published by Springer-Verlag. This book was released on 2019-06-28 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dieses Buch ebnet dem Leser einen kleinschrittigen und somit gut begehbaren Weg in die algebraische Geometrie. Zentrale Begriffe und Ergebnisse aus kommutativer Algebra und algebraischer Geometrie werden vorgestellt und bilden eine solide Grundlage, um tiefer in die Materie einzusteigen und auch aktuelle Forschungsliteratur selbstständig zu verstehen. Auch wenn einige Beweise dem Leser überlassen bleiben, ist das Werk bestens zum Nachschlagen geeignet und die Darstellung weitgehend in sich abgeschlossen, externe Referenzen wurden auf ein Mindestmaß beschränkt. Der Inhalt Das Buch führt von Kategorientheorie, homologischer und kommutativer Algebra schließlich zur Schematheorie und Garbenkohomologie. Wegmarken, denen der Leser dabei begegnen wird, sind unter anderem: affine und projektive Schemata, Grundtypen von Morphismen, Faserprodukt, Dimensionstheorie, quasikohärente Garben, Varietäten, allgemeiner Satz von Bezout, Divisoren, Aufblasungen, Kähler-Differentiale, Čech-Kohomologie und Kohomologie der projektiven Räume, Ext-Garben, flache und glatte Morphismen, höhere direkte Bildgarben, Dualität und Halbstetigkeitssätze. Der Leser sollte bereits grundlegende Kenntnisse aus der Algebra mitbringen, etwa zu Gruppen-, Körper- und Galoistheorie sowie Determinanten, Resultanten und elementaren Ergebnissen über Polynomringe. Ebenfalls notwendig ist eine gewisse Vertrautheit mit Begriffen der allgemeinen mengentheoretischen Topologie.

Commutative Algebra - Proceedings Of The Workshop

Author : Giuseppe Valla
Publisher : World Scientific
ISBN 13 : 9814551791
Total Pages : 330 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Commutative Algebra - Proceedings Of The Workshop by : Giuseppe Valla

Download or read book Commutative Algebra - Proceedings Of The Workshop written by Giuseppe Valla and published by World Scientific. This book was released on 1994-08-19 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a relatively short time, commutative algebra has grown in many directions. Over a period of nearly fifty years starting from the so-called homological period till today, the area has developed into a rich laboratory of methods, structures and problem-solving tools.One could say a distinct modern trend of commutative algebra is a strong interaction with various aspects of Combinatorics and Computer Algebra. This has resulted in a new sense of measuring for old assumptions, and a better understanding of old results.At the same time, Invariant Theory and Algebraic Geometry remain constituents of an everlasting classical source, responsible for important themes that have been developed in Commutative Algebra — such as deformation, linkage, algebraic tori and determinantal rings, etc.This volume of proceedings is well-entrenched on the lines of development outlined above. As such, it aims to keep researchers and mathematicians well-informed of the developments in the field.

Formal Concept Analysis

Author : Bernhard Ganter
Publisher : Springer
ISBN 13 : 354031881X
Total Pages : 349 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Formal Concept Analysis by : Bernhard Ganter

Download or read book Formal Concept Analysis written by Bernhard Ganter and published by Springer. This book was released on 2005-07-11 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Formal concept analysis has been developed as a field of applied mathematics based on the mathematization of concept and concept hierarchy. It thereby allows us to mathematically represent, analyze, and construct conceptual structures. The formal concept analysis approach has been proven successful in a wide range of application fields. This book constitutes a comprehensive and systematic presentation of the state of the art of formal concept analysis and its applications. The first part of the book is devoted to foundational and methodological topics. The contributions in the second part demonstrate how formal concept analysis is successfully used outside of mathematics, in linguistics, text retrieval, association rule mining, data analysis, and economics. The third part presents applications in software engineering.

Local Analytic Geometry

Author : Theo de Jong
Publisher : Vieweg+Teubner Verlag
ISBN 13 : 9783528031374
Total Pages : 384 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Local Analytic Geometry by : Theo de Jong

Download or read book Local Analytic Geometry written by Theo de Jong and published by Vieweg+Teubner Verlag. This book was released on 2000-04-27 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Auf der Grundlage einer Einführung in die kommutative Algebra, algebraische Geometrie und komplexe Analysis werden zunächst Kurvensingularitäten untersucht. Daran schließen Ergebnisse an, die zum ersten Mal in einem Lehrbuch aufgenommen wurden, das Verhalten von Invarianten in Familien, Standardbasen für konvergente Potenzreihenringe, Approximationssätze, Grauerts Satz über die Existenz der versellen Deformation. Das Buch richtet sich an Studenten höherer Semester, Doktoranden und Dozenten. Es ist auf der Grundlage mehrerer Vorlesungen und Seminaren an den Universitäten in Kaiserslautern und Saarbrücken entstanden.

A Singular Introduction to Commutative Algebra

Author : Gert-Martin Greuel
Publisher : Springer Science & Business Media
ISBN 13 : 3662049635
Total Pages : 601 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis A Singular Introduction to Commutative Algebra by : Gert-Martin Greuel

Download or read book A Singular Introduction to Commutative Algebra written by Gert-Martin Greuel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book can be understood as a model for teaching commutative algebra, and takes into account modern developments such as algorithmic and computational aspects. As soon as a new concept is introduced, the authors show how the concept can be worked on using a computer. The computations are exemplified with the computer algebra system Singular, developed by the authors. Singular is a special system for polynomial computation with many features for global as well as for local commutative algebra and algebraic geometry. The book includes a CD containing Singular as well as the examples and procedures explained in the book.

Traces of Differential Forms and Hochschild Homology

Author : Reinhold Hübl
Publisher : Springer
ISBN 13 : 3540461256
Total Pages : 115 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Traces of Differential Forms and Hochschild Homology by : Reinhold Hübl

Download or read book Traces of Differential Forms and Hochschild Homology written by Reinhold Hübl and published by Springer. This book was released on 2006-12-08 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an introduction to, as well as a unification and extension of the published work and some unpublished ideas of J. Lipman and E. Kunz about traces of differential forms and their relations to duality theory for projective morphisms. The approach uses Hochschild-homology, the definition of which is extended to the category of topological algebras. Many results for Hochschild-homology of commutative algebras also hold for Hochschild-homology of topological algebras. In particular, after introducing an appropriate notion of completion of differential algebras, one gets a natural transformation between differential forms and Hochschild-homology of topological algebras. Traces of differential forms are of interest to everyone working with duality theory and residue symbols. Hochschild-homology is a useful tool in many areas of k-theory. The treatment is fairly elementary and requires only little knowledge in commutative algebra and algebraic geometry.

Resolution of Curve and Surface Singularities in Characteristic Zero

Author : K. Kiyek
Publisher : Springer Science & Business Media
ISBN 13 : 1402020295
Total Pages : 506 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Resolution of Curve and Surface Singularities in Characteristic Zero by : K. Kiyek

Download or read book Resolution of Curve and Surface Singularities in Characteristic Zero written by K. Kiyek and published by Springer Science & Business Media. This book was released on 2012-09-11 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. •• . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it • To solve the problem, it is enough to consider a special kind of Cremona trans formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.

Intersection Theory

Author : William Fulton
Publisher : Springer Science & Business Media
ISBN 13 : 1461217008
Total Pages : 483 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Intersection Theory by : William Fulton

Download or read book Intersection Theory written by William Fulton and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intersection theory has played a central role in mathematics, from the ancient origins of algebraic geometry in the solutions of polynomial equations to the triumphs of algebraic geometry during the last two centuries. This book develops the foundations of the theory and indicates the range of classical and modern applications. The hardcover edition received the prestigious Steele Prize in 1996 for best exposition.

The Mathematics of Networks of Linear Systems

Author : Paul A. Fuhrmann
Publisher : Springer
ISBN 13 : 3319166468
Total Pages : 662 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis The Mathematics of Networks of Linear Systems by : Paul A. Fuhrmann

Download or read book The Mathematics of Networks of Linear Systems written by Paul A. Fuhrmann and published by Springer. This book was released on 2015-05-26 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the mathematical foundations of networks of linear control systems, developed from an algebraic systems theory perspective. This includes a thorough treatment of questions of controllability, observability, realization theory, as well as feedback control and observer theory. The potential of networks for linear systems in controlling large-scale networks of interconnected dynamical systems could provide insight into a diversity of scientific and technological disciplines. The scope of the book is quite extensive, ranging from introductory material to advanced topics of current research, making it a suitable reference for graduate students and researchers in the field of networks of linear systems. Part I can be used as the basis for a first course in Algebraic System Theory, while Part II serves for a second, advanced, course on linear systems. Finally, Part III, which is largely independent of the previous parts, is ideally suited for advanced research seminars aimed at preparing graduate students for independent research. “Mathematics of Networks of Linear Systems” contains a large number of exercises and examples throughout the text making it suitable for graduate courses in the area.

An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces

Author : Martin Schlichenmaier
Publisher : Springer Science & Business Media
ISBN 13 : 3540711759
Total Pages : 217 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces by : Martin Schlichenmaier

Download or read book An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces written by Martin Schlichenmaier and published by Springer Science & Business Media. This book was released on 2010-02-11 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to modern geometry. Starting from an elementary level, the author develops deep geometrical concepts that play an important role in contemporary theoretical physics, presenting various techniques and viewpoints along the way. This second edition contains two additional, more advanced geometric techniques: the modern language and modern view of Algebraic Geometry and Mirror Symmetry.

Modular Lie Algebras and their Representations

Author : H. Strade
Publisher : CRC Press
ISBN 13 : 9780824775940
Total Pages : 326 pages
Book Rating : 4.7/5 (759 download)

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Book Synopsis Modular Lie Algebras and their Representations by : H. Strade

Download or read book Modular Lie Algebras and their Representations written by H. Strade and published by CRC Press. This book was released on 1988-01-29 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an introduction to the structure and representation theory of modular Lie algebras over fields of positive characteristic. It introduces the beginner to the theory of modular Lie algebras and is meant to be a reference text for researchers.

Complete Intersections

Author : S. Greco
Publisher : Springer
ISBN 13 : 3540390898
Total Pages : 309 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Complete Intersections by : S. Greco

Download or read book Complete Intersections written by S. Greco and published by Springer. This book was released on 2006-12-08 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraische Geometrie

Author : Markus Brodmann
Publisher : Springer-Verlag
ISBN 13 : 3034892667
Total Pages : 485 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Algebraische Geometrie by : Markus Brodmann

Download or read book Algebraische Geometrie written by Markus Brodmann and published by Springer-Verlag. This book was released on 2013-03-07 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diese Einführung in die algebraische Geometrie richtet sich an Studierende mittlere und höhere Semester. Vorausgesetzt werden lediglich die im ersten Studienjahr erworbenen Grundkenntnisse. Ausgehend von den affinen Hyperflächen werden beliebige affine und schliesslich projektive Varietäten untersucht. Die benötigte Algebra wird dabei laufend entwickelt. Schwerpunkte des Buches sind die Dimensions- und Morphismentheorie, die Multiplizitätstheorie sowie der Gradbegriff. Zahlreiche Beispiele sollen dem Leser helfen, sich über die konkrete Bedeutung des Stoffes klarzuwerden.