Commutative Algebra And Algebraic Geometry


Commutative Algebra And Algebraic Geometry
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Algebraic Geometry And Commutative Algebra


Algebraic Geometry And Commutative Algebra
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Author : Siegfried Bosch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-15

Algebraic Geometry And Commutative Algebra written by Siegfried Bosch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-15 with Mathematics categories.


Algebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry, like algebraic number theory. The new techniques paved the way to spectacular progress such as the proof of Fermat’s Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts. More advanced readers can use the book to broaden their view on the subject. A separate part deals with the necessary prerequisites from commutative algebra. On a whole, the book provides a very accessible and self-contained introduction to algebraic geometry, up to a quite advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. This way the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature.



Commutative Algebra


Commutative Algebra
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Author : David Eisenbud
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-03-30

Commutative Algebra written by David Eisenbud and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-30 with Mathematics categories.


This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.



Commutative Algebra Algebraic Geometry And Computational Methods


Commutative Algebra Algebraic Geometry And Computational Methods
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Author : David Eisenbud
language : en
Publisher: Springer
Release Date : 1999-07

Commutative Algebra Algebraic Geometry And Computational Methods written by David Eisenbud and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07 with Mathematics categories.


This volume contains papers presented at the International Conference on Commutative Algebra, Algebraic geometry, and Computational methods held in Hanoi in 1996, as well as papers written subsequently. It features both expository articles as well as research papers on a range of currently active areas in commutative algebra, algebraic geometry (particularly surveys on intersection theory) and combinatorics. In addition, a special feature is a section on the life and work of Wolfgang Vogel, who was an organiser of the conference.



Introduction To Commutative Algebra And Algebraic Geometry


Introduction To Commutative Algebra And Algebraic Geometry
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Author : Ernst Kunz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-06

Introduction To Commutative Algebra And Algebraic Geometry written by Ernst Kunz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-06 with Mathematics categories.


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.



Introduction To Algebraic Geometry And Commutative Algebra


Introduction To Algebraic Geometry And Commutative Algebra
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Author : Dilip P. Patil
language : en
Publisher: World Scientific
Release Date : 2010

Introduction To Algebraic Geometry And Commutative Algebra written by Dilip P. Patil and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.


Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. With concise yet clear definitions and synopses a selection is made from the wealth of meterial in the disciplines including the Riemann-Roch theorem for arbitrary projective curves."--pub. desc.



Commutative Algebra


Commutative Algebra
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Author : David Eisenbud
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Commutative Algebra written by David Eisenbud and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.


This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.



Commutative Algebra And Algebraic Geometry


Commutative Algebra And Algebraic Geometry
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Author : Sudhir Ghorpade
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Commutative Algebra And Algebraic Geometry written by Sudhir Ghorpade and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.


The first Joint AMS-India Mathematics Meeting was held in Bangalore (India). This book presents articles written by speakers from a special session on commutative algebra and algebraic geometry. Included are contributions from some leading researchers around the world in this subject area. The volume contains new and original research papers and survey articles suitable for graduate students and researchers interested in commutative algebra and algebraic geometry.



Algebraic K Theory Commutative Algebra And Algebraic Geometry


Algebraic K Theory Commutative Algebra And Algebraic Geometry
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Author : R. Keith Dennis
language : en
Publisher: American Mathematical Soc.
Release Date : 1992

Algebraic K Theory Commutative Algebra And Algebraic Geometry written by R. Keith Dennis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.


In the mid-1960s, several Italian mathematicians began to study the connections between classical arguments in commutative algebra and algebraic geometry, and the contemporaneous development of algebraic $K$-theory in the U.S. These connections were exemplified by the work of Andreotti-Bombieri, Salmon, and Traverso on seminormality, and by Bass-Murthy on the Picard groups of polynomial rings. Interactions proceeded far beyond this initial point to encompass Chow groups of singular varieties, complete intersections, and applications of $K$-theory to arithmetic and real geometry. This volume contains the proceedings from a U.S.-Italy Joint Summer Seminar, which focused on this circle of ideas. The conference, held in June 1989 in Santa Margherita Ligure, Italy, was supported jointly by the Consiglio Nazionale delle Ricerche and the National Science Foundation. The book contains contributions from some of the leading experts in this area.



Commutative Algebra And Its Interactions To Algebraic Geometry


Commutative Algebra And Its Interactions To Algebraic Geometry
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Author : Nguyen Tu CUONG
language : en
Publisher: Springer
Release Date : 2018-08-02

Commutative Algebra And Its Interactions To Algebraic Geometry written by Nguyen Tu CUONG and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-02 with Mathematics categories.


This book presents four lectures on recent research in commutative algebra and its applications to algebraic geometry. Aimed at researchers and graduate students with an advanced background in algebra, these lectures were given during the Commutative Algebra program held at the Vietnam Institute of Advanced Study in Mathematics in the winter semester 2013 -2014. The first lecture is on Weyl algebras (certain rings of differential operators) and their D-modules, relating non-commutative and commutative algebra to algebraic geometry and analysis in a very appealing way. The second lecture concerns local systems, their homological origin, and applications to the classification of Artinian Gorenstein rings and the computation of their invariants. The third lecture is on the representation type of projective varieties and the classification of arithmetically Cohen -Macaulay bundles and Ulrich bundles. Related topics such as moduli spaces of sheaves, liaison theory, minimal resolutions, and Hilbert schemes of points are also covered. The last lecture addresses a classical problem: how many equations are needed to define an algebraic variety set-theoretically? It systematically covers (and improves) recent results for the case of toric varieties.



Introduction To Commutative Algebra And Algebraic Geometry


Introduction To Commutative Algebra And Algebraic Geometry
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Author : Ernst Kunz
language : en
Publisher: Birkhäuser
Release Date : 1984

Introduction To Commutative Algebra And Algebraic Geometry written by Ernst Kunz and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.


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.