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The Red Book of Varieties and Schemes

The Red Book of Varieties and Schemes PDF Author: David Mumford
Publisher: Springer
ISBN: 3540460217
Category : Mathematics
Languages : en
Pages : 314

Book Description
Mumford's famous "Red Book" gives a simple, readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduates or mathematicians in other fields wishing to quickly learn aboutalgebraic geometry. This new edition includes an appendix that gives an overview of the theory of curves, their moduli spaces and their Jacobians -- one of the most exciting fields within algebraic geometry.

The Red Book of Varieties and Schemes

The Red Book of Varieties and Schemes PDF Author: David Mumford
Publisher: Springer
ISBN: 3540460217
Category : Mathematics
Languages : en
Pages : 314

Book Description
Mumford's famous "Red Book" gives a simple, readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduates or mathematicians in other fields wishing to quickly learn aboutalgebraic geometry. This new edition includes an appendix that gives an overview of the theory of curves, their moduli spaces and their Jacobians -- one of the most exciting fields within algebraic geometry.

Algebraic Curves and One-dimensional Fields

Algebraic Curves and One-dimensional Fields PDF Author: Fedor Bogomolov
Publisher: American Mathematical Soc.
ISBN: 9780821883488
Category : Mathematics
Languages : en
Pages : 232

Book Description
Algebraic curves have many special properties that make their study particularly rewarding. As a result, curves provide a natural introduction to algebraic geometry. In this book, the authors also bring out aspects of curves that are unique to them and emphasize connections with algebra. This text covers the essential topics in the geometry of algebraic curves, such as line bundles and vector bundles, the Riemann-Roch Theorem, divisors, coherent sheaves, and zeroth and firstcohomology groups. The authors make a point of using concrete examples and explicit methods to ensure that the style is clear and understandable. Several chapters develop the connections between the geometry of algebraic curves and the algebra of one-dimensional fields. This is an interesting topic that israrely found in introductory texts on algebraic geometry. This book makes an excellent text for a first course for graduate students.

The Geometry of Schemes

The Geometry of Schemes PDF Author: David Eisenbud
Publisher: Springer Science & Business Media
ISBN: 0387226397
Category : Mathematics
Languages : en
Pages : 300

Book Description
Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Algebraic Geometry

Algebraic Geometry PDF Author: Thomas A. Garrity
Publisher: American Mathematical Soc.
ISBN: 0821893963
Category : Mathematics
Languages : en
Pages : 335

Book Description
Algebraic Geometry has been at the center of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas. This text consists of a series of ex

Using the Mathematics Literature

Using the Mathematics Literature PDF Author: Kristine K. Fowler
Publisher: CRC Press
ISBN: 9780824750350
Category : Language Arts & Disciplines
Languages : en
Pages : 412

Book Description
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.

The Grassmannian Variety

The Grassmannian Variety PDF Author: V. Lakshmibai
Publisher: Springer
ISBN: 1493930826
Category : Mathematics
Languages : en
Pages : 172

Book Description
This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads of commutative algebra, algebraic geometry, representation theory, and combinatorics. Therefore, this text uniquely presents an exciting playing field for graduate students and researchers in mathematics, physics, and computer science, to expand their knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for the Grassmannian varieties and their Schubert subvarieties are introduced and the text presents some important applications of SMT including the Cohen–Macaulay property, normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. This text would serve well as a reference book for a graduate work on Grassmannian varieties and would be an excellent supplementary text for several courses including those in geometry of spherical varieties, Schubert varieties, advanced topics in geometric and differential topology, representation theory of compact and reductive groups, Lie theory, toric varieties, geometric representation theory, and singularity theory. The reader should have some familiarity with commutative algebra and algebraic geometry.

80 Years of Zentralblatt MATH

80 Years of Zentralblatt MATH PDF Author: Olaf Teschke
Publisher: Springer Science & Business Media
ISBN: 3642211720
Category : Mathematics
Languages : en
Pages : 194

Book Description
Founded in 1931 by Otto Neugebauer as the printed documentation service “Zentralblatt für Mathematik und ihre Grenzgebiete”, Zentralblatt MATH (ZBMATH) celebrates its 80th anniversary in 2011. Today it is the most comprehensive and active reference database in pure and applied mathematics worldwide. Many prominent mathematicians have been involved in this service as reviewers or editors and have, like all mathematicians, left their footprints in ZBMATH, in a long list of entries describing all of their research publications in mathematics. This book provides one review from each of the 80 years of ZBMATH. Names like Courant, Kolmogorov, Hardy, Hirzebruch, Faltings and many others can be found here. In addition to the original reviews, the book offers the authors' profiles indicating their co-authors, their favorite journals and the time span of their publication activities. In addition to this, a generously illustrated essay by Silke Göbel describes the history of ZBMATH.

A Concise Introduction to Algebraic Varieties

A Concise Introduction to Algebraic Varieties PDF Author: Brian Osserman
Publisher: American Mathematical Society
ISBN: 1470466651
Category : Mathematics
Languages : en
Pages : 259

Book Description


Illustrating Mathematics

Illustrating Mathematics PDF Author: Diana Davis
Publisher: American Mathematical Soc.
ISBN: 1470461226
Category : Education
Languages : en
Pages : 171

Book Description
This book is for anyone who wishes to illustrate their mathematical ideas, which in our experience means everyone. It is organized by material, rather than by subject area, and purposefully emphasizes the process of creating things, including discussions of failures that occurred along the way. As a result, the reader can learn from the experiences of those who came before, and will be inspired to create their own illustrations. Topics illustrated within include prime numbers, fractals, the Klein bottle, Borromean rings, tilings, space-filling curves, knot theory, billiards, complex dynamics, algebraic surfaces, groups and prime ideals, the Riemann zeta function, quadratic fields, hyperbolic space, and hyperbolic 3-manifolds. Everyone who opens this book should find a type of mathematics with which they identify. Each contributor explains the mathematics behind their illustration at an accessible level, so that all readers can appreciate the beauty of both the object itself and the mathematics behind it.

Representations of Algebras and Related Topics

Representations of Algebras and Related Topics PDF Author: Andrzej Skowroński
Publisher: European Mathematical Society
ISBN: 9783037191019
Category : Mathematics
Languages : en
Pages : 744

Book Description
This book, which explores recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, combinatorics, quantum algebras, and theoretical field, is conceived as a handbook to provide easy access to the present state of knowledge and stimulate further development. The many topics discussed include quivers, quivers with potential, bound quiver algebras, Jacobian algebras, cluster algebras and categories, Calabi-Yau algebras and categories, triangulated and derived categories, and quantum loop algebras. This book consists of thirteen self-contained expository survey and research articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. The articles contain a large number of examples and open problems and give new perspectives for research in the field.

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