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Author : Brian Osserman
Publisher : American Mathematical Society
ISBN 13 : 1470466651
Total Pages : 259 pages
Book Rating : 4.57/5 ( download)
Download or read book A Concise Introduction to Algebraic Varieties written by Brian Osserman and published by American Mathematical Society. This book was released on 2021-12-06 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. P. May
Publisher : University of Chicago Press
ISBN 13 : 9780226511832
Total Pages : 262 pages
Book Rating : 4.39/5 ( download)
Download or read book A Concise Course in Algebraic Topology written by J. P. May and published by University of Chicago Press. This book was released on 1999-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
Author : Serge Lang
Publisher : Courier Dover Publications
ISBN 13 : 048683980X
Total Pages : 273 pages
Book Rating : 4.06/5 ( download)
Download or read book Introduction to Algebraic Geometry written by Serge Lang and published by Courier Dover Publications. This book was released on 2019-03-20 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.
Author : Brian Osserman
Publisher : American Mathematical Society
ISBN 13 : 1470460130
Total Pages : 259 pages
Book Rating : 4.36/5 ( download)
Download or read book A Concise Introduction to Algebraic Varieties written by Brian Osserman and published by American Mathematical Society. This book was released on 2021-12-02 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Concise Introduction to Algebraic Varieties is designed for a one-term introductory course on algebraic varieties over an algebraically closed field, and it provides a solid basis for a course on schemes and cohomology or on specialized topics, such as toric varieties and moduli spaces of curves. The book balances generality and accessibility by presenting local and global concepts, such as nonsingularity, normality, and completeness using the language of atlases, an approach that is most commonly associated with differential topology. The book concludes with a discussion of the Riemann-Roch theorem, the Brill-Noether theorem, and applications. The prerequisites for the book are a strong undergraduate algebra course and a working familiarity with basic point-set topology. A course in graduate algebra is helpful but not required. The book includes appendices presenting useful background in complex analytic topology and commutative algebra and provides plentiful examples and exercises that help build intuition and familiarity with algebraic varieties.
Author : Géza Schay
Publisher : Springer Science & Business Media
ISBN 13 : 0817683259
Total Pages : 338 pages
Book Rating : 4.52/5 ( download)
Download or read book A Concise Introduction to Linear Algebra written by Géza Schay and published by Springer Science & Business Media. This book was released on 2012-03-30 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the author's previous edition on the subject (Introduction to Linear Algebra, Jones & Bartlett, 1996), this book offers a refreshingly concise text suitable for a standard course in linear algebra, presenting a carefully selected array of essential topics that can be thoroughly covered in a single semester. Although the exposition generally falls in line with the material recommended by the Linear Algebra Curriculum Study Group, it notably deviates in providing an early emphasis on the geometric foundations of linear algebra. This gives students a more intuitive understanding of the subject and enables an easier grasp of more abstract concepts covered later in the course. The focus throughout is rooted in the mathematical fundamentals, but the text also investigates a number of interesting applications, including a section on computer graphics, a chapter on numerical methods, and many exercises and examples using MATLAB. Meanwhile, many visuals and problems (a complete solutions manual is available to instructors) are included to enhance and reinforce understanding throughout the book. Brief yet precise and rigorous, this work is an ideal choice for a one-semester course in linear algebra targeted primarily at math or physics majors. It is a valuable tool for any professor who teaches the subject.
Author : Andrew H. Wallace
Publisher : Courier Corporation
ISBN 13 : 0486799905
Total Pages : 128 pages
Book Rating : 4.02/5 ( download)
Download or read book Homology Theory on Algebraic Varieties written by Andrew H. Wallace and published by Courier Corporation. This book was released on 2014-10-27 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise and authoritative monograph, geared toward advanced undergraduate and graduate students, covers linear sections, singular and hyperplane sections, Lefschetz's first and second theorems, the Poincaré formula, and invariant and relative cycles. 1958 edition.
Author : G. Kempf
Publisher : Cambridge University Press
ISBN 13 : 9780521426138
Total Pages : 180 pages
Book Rating : 4.38/5 ( download)
Download or read book Algebraic Varieties written by G. Kempf and published by Cambridge University Press. This book was released on 1993-09-09 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint.
Author : David A. Cox
Publisher : American Mathematical Soc.
ISBN 13 : 0821848194
Total Pages : 874 pages
Book Rating : 4.97/5 ( download)
Download or read book Toric Varieties written by David A. Cox and published by American Mathematical Soc.. This book was released on 2011 with total page 874 pages. Available in PDF, EPUB and Kindle. Book excerpt: Toric varieties form a beautiful and accessible part of modern algebraic geometry. This book covers the standard topics in toric geometry; a novel feature is that each of the first nine chapters contains an introductory section on the necessary background material in algebraic geometry. Other topics covered include quotient constructions, vanishing theorems, equivariant cohomology, GIT quotients, the secondary fan, and the minimal model program for toric varieties. The subject lends itself to rich examples reflected in the 134 illustrations included in the text. The book also explores connections with commutative algebra and polyhedral geometry, treating both polytopes and their unbounded cousins, polyhedra. There are appendices on the history of toric varieties and the computational tools available to investigate nontrivial examples in toric geometry. Readers of this book should be familiar with the material covered in basic graduate courses in algebra and topology, and to a somewhat lesser degree, complex analysis. In addition, the authors assume that the reader has had some previous experience with algebraic geometry at an advanced undergraduate level. The book will be a useful reference for graduate students and researchers who are interested in algebraic geometry, polyhedral geometry, and toric varieties.
Author : Shihoko Ishii
Publisher : Springer
ISBN 13 : 443155081X
Total Pages : 227 pages
Book Rating : 4.15/5 ( download)
Download or read book Introduction to Singularities written by Shihoko Ishii and published by Springer. This book was released on 2014-11-19 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. Another example is that the moduli spaces of varieties have natural compactification, the boundaries of which correspond to singular varieties. A remarkable fact is that the study of singularities is developing and people are beginning to see that singularities are interesting and can be handled by human beings. This book is a handy introduction to singularities for anyone interested in singularities. The focus is on an isolated singularity in an algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dim ensional isolated singularities are introduced. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied.
Author : Klaus Hulek
Publisher : American Mathematical Soc.
ISBN 13 : 0821829521
Total Pages : 225 pages
Book Rating : 4.23/5 ( download)
Download or read book Elementary Algebraic Geometry written by Klaus Hulek and published by American Mathematical Soc.. This book was released on 2003 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a true introduction to the basic concepts and techniques of algebraic geometry. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory. The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary.
