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Author: David Eisenbud
Publisher: Springer Science & Business Media
ISBN: 0387264566
Category : Mathematics
Languages : en
Pages : 254
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Book Description
First textbook-level account of basic examples and techniques in this area. Suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already. David Eisenbud is a well-known mathematician and current president of the American Mathematical Society, as well as a successful Springer author.
Author: David Eisenbud
Publisher: Springer Science & Business Media
ISBN: 0387264566
Category : Mathematics
Languages : en
Pages : 254
Get Book Here
Book Description
First textbook-level account of basic examples and techniques in this area. Suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already. David Eisenbud is a well-known mathematician and current president of the American Mathematical Society, as well as a successful Springer author.
Author: F.E.A. Johnson
Publisher: Springer Science & Business Media
ISBN: 1447122941
Category : Mathematics
Languages : en
Pages : 307
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Book Description
The most important invariant of a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familiar. In the general case, however, homotopy theory over nontrivial fundamental groups is much more problematic and far less well understood. Syzygies and Homotopy Theory explores the problem of nonsimply connected homotopy in the first nontrivial cases and presents, for the first time, a systematic rehabilitation of Hilbert's method of syzygies in the context of non-simply connected homotopy theory. The first part of the book is theoretical, formulated to allow a general finitely presented group as a fundamental group. The innovation here is to regard syzygies as stable modules rather than minimal modules. Inevitably this forces a reconsideration of the problems of noncancellation; these are confronted in the second, practical, part of the book. In particular, the second part of the book considers how the theory works out in detail for the specific examples Fn ́F where Fn is a free group of rank n and F is finite. Another innovation is to parametrize the first syzygy in terms of the more familiar class of stably free modules. Furthermore, detailed description of these stably free modules is effected by a suitable modification of the method of Milnor squares. The theory developed within this book has potential applications in various branches of algebra, including homological algebra, ring theory and K-theory. Syzygies and Homotopy Theory will be of interest to researchers and also to graduate students with a background in algebra and algebraic topology.
Author: Jerzy Weyman
Publisher: Cambridge University Press
ISBN: 9780521621977
Category : Mathematics
Languages : en
Pages : 404
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Book Description
The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott's Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method.
Author: Irena Peeva
Publisher: CRC Press
ISBN: 1420050915
Category : Mathematics
Languages : en
Pages : 305
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Book Description
Hilbert functions and resolutions are both central objects in commutative algebra and fruitful tools in the fields of algebraic geometry, combinatorics, commutative algebra, and computational algebra. Spurred by recent research in this area, Syzygies and Hilbert Functions explores fresh developments in the field as well as fundamental concepts.
Author: Shaun Bullett
Publisher: World Scientific
ISBN: 1786341093
Category : Mathematics
Languages : en
Pages : 235
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Book Description
This book leads readers from a basic foundation to an advanced level understanding of geometry in advanced pure mathematics. Chapter by chapter, readers will be led from a foundation level understanding to advanced level understanding. This is the perfect text for graduate or PhD mathematical-science students looking for support in algebraic geometry, geometric group theory, modular group, holomorphic dynamics and hyperbolic geometry, syzygies and minimal resolutions, and minimal surfaces.Geometry in Advanced Pure Mathematics is the fourth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.
Author: David Eisenbud
Publisher: Springer Science & Business Media
ISBN: 1461253500
Category : Mathematics
Languages : en
Pages : 784
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Book Description
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.
Author: Michel Brion
Publisher: Springer Science & Business Media
ISBN: 0817644059
Category : Mathematics
Languages : en
Pages : 259
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Book Description
Systematically develops the theory of Frobenius splittings and covers all its major developments. Concise, efficient exposition unfolds from basic introductory material on Frobenius splittings—definitions, properties and examples—to cutting edge research.
Author: David A. Cox
Publisher: Springer Science & Business Media
ISBN: 1475769113
Category : Mathematics
Languages : en
Pages : 513
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Book Description
An illustration of the many uses of algebraic geometry, highlighting the more recent applications of Groebner bases and resultants. Along the way, the authors provide an introduction to some algebraic objects and techniques more advanced than typically encountered in a first course. The book is accessible to non-specialists and to readers with a diverse range of backgrounds, assuming readers know the material covered in standard undergraduate courses, including abstract algebra. But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.
Author: E. Graham Evans
Publisher: Cambridge University Press
ISBN: 0521314119
Category : Mathematics
Languages : en
Pages : 137
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Book Description
This 1985 book covers from first principles the theory of Syzygies.
Author: David Eisenbud
Publisher: Cambridge University Press
ISBN: 1107017084
Category : Mathematics
Languages : en
Pages : 633
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Book Description
3264, the mathematical solution to a question concerning geometric figures.
