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An Introduction To Algebraic Geometry
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Book Synopsis Introduction to Algebraic Geometry by : Steven Dale Cutkosky
Download or read book Introduction to Algebraic Geometry written by Steven Dale Cutkosky and published by American Mathematical Soc.. This book was released on 2018-06-01 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters. With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.
Book Synopsis Algebraic Geometry by : Robin Hartshorne
Download or read book Algebraic Geometry written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Book Synopsis Introduction to Algebraic Geometry by : Serge Lang
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.
Book Synopsis Introduction to Algebraic Geometry by : Brendan Hassett
Download or read book Introduction to Algebraic Geometry written by Brendan Hassett and published by Cambridge University Press. This book was released on 2007-05-03 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry, central to pure mathematics, has important applications in such fields as engineering, computer science, statistics and computational biology, which exploit the computational algorithms that the theory provides. Users get the full benefit, however, when they know something of the underlying theory, as well as basic procedures and facts. This book is a systematic introduction to the central concepts of algebraic geometry most useful for computation. Written for advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and restricts development of formalism to what is needed to address these examples. In particular, it introduces the notion of Gröbner bases early on and develops algorithms for almost everything covered. It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer science, biomathematics and bioinformatics.
Book Synopsis Introduction to Algebraic Geometry by : Igor Kriz
Download or read book Introduction to Algebraic Geometry written by Igor Kriz and published by Springer Nature. This book was released on 2021-03-13 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to provide an introduction to algebraic geometry accessible to students. Starting from solutions of polynomial equations, modern tools of the subject soon appear, motivated by how they improve our understanding of geometrical concepts. In many places, analogies and differences with related mathematical areas are explained. The text approaches foundations of algebraic geometry in a complete and self-contained way, also covering the underlying algebra. The last two chapters include a comprehensive treatment of cohomology and discuss some of its applications in algebraic geometry.
Book Synopsis An Invitation to Algebraic Geometry by : Karen E. Smith
Download or read book An Invitation to Algebraic Geometry written by Karen E. Smith and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a description of the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.
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 253 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.
Book Synopsis Algebraic Geometry by : Solomon Lefschetz
Download or read book Algebraic Geometry written by Solomon Lefschetz and published by Courier Corporation. This book was released on 2012-09-05 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Book Synopsis Algebraic Geometry by : Daniel Perrin
Download or read book Algebraic Geometry written by Daniel Perrin and published by Springer Science & Business Media. This book was released on 2007-12-16 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject; it assumes only the standard background of undergraduate algebra. The book starts with easily-formulated problems with non-trivial solutions and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.
Book Synopsis An Undergraduate Primer in Algebraic Geometry by : Ciro Ciliberto
Download or read book An Undergraduate Primer in Algebraic Geometry written by Ciro Ciliberto and published by Springer Nature. This book was released on 2021-05-05 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of two parts. The first is devoted to an introduction to basic concepts in algebraic geometry: affine and projective varieties, some of their main attributes and examples. The second part is devoted to the theory of curves: local properties, affine and projective plane curves, resolution of singularities, linear equivalence of divisors and linear series, Riemann–Roch and Riemann–Hurwitz Theorems. The approach in this book is purely algebraic. The main tool is commutative algebra, from which the needed results are recalled, in most cases with proofs. The prerequisites consist of the knowledge of basics in affine and projective geometry, basic algebraic concepts regarding rings, modules, fields, linear algebra, basic notions in the theory of categories, and some elementary point–set topology. This book can be used as a textbook for an undergraduate course in algebraic geometry. The users of the book are not necessarily intended to become algebraic geometers but may be interested students or researchers who want to have a first smattering in the topic. The book contains several exercises, in which there are more examples and parts of the theory that are not fully developed in the text. Of some exercises, there are solutions at the end of each chapter.
Book Synopsis An Introduction to Algebraic Geometry and Algebraic Groups by : Meinolf Geck
Download or read book An Introduction to Algebraic Geometry and Algebraic Groups written by Meinolf Geck and published by Oxford University Press. This book was released on 2013-03-14 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields.
Book Synopsis Introduction to Algebraic Geometry by : Justin R. Smith
Download or read book Introduction to Algebraic Geometry written by Justin R. Smith and published by Justin Smith. This book was released on 2014 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for self-study or as a textbook for graduate students or advanced undergraduates. It presupposes some basic knowledge of point-set topology and a solid foundation in linear algebra. Otherwise, it develops all of the commutative algebra, sheaf-theory and cohomology needed to understand the material. It also presents applications to robotics and other fields.
Book Synopsis Computational Algebraic Geometry by : Hal Schenck
Download or read book Computational Algebraic Geometry written by Hal Schenck and published by Cambridge University Press. This book was released on 2003-10-06 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interplay between algebra and geometry is a beautiful (and fun!) area of mathematical investigation. Advances in computing and algorithms make it possible to tackle many classical problems in a down-to-earth and concrete fashion. This opens wonderful new vistas and allows us to pose, study and solve problems that were previously out of reach. Suitable for graduate students, the objective of this 2003 book is to bring advanced algebra to life with lots of examples. The first chapters provide an introduction to commutative algebra and connections to geometry. The rest of the book focuses on three active areas of contemporary algebra: Homological Algebra (the snake lemma, long exact sequence inhomology, functors and derived functors (Tor and Ext), and double complexes); Algebraic Combinatorics and Algebraic Topology (simplicial complexes and simplicial homology, Stanley-Reisner rings, upper bound theorem and polytopes); and Algebraic Geometry (points and curves in projective space, Riemann-Roch, Cech cohomology, regularity).
Book Synopsis Algebra & Geometry by : Mark V. Lawson
Download or read book Algebra & Geometry written by Mark V. Lawson and published by CRC Press. This book was released on 2016-11-25 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra & Geometry: An Introduction to University Mathematics provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical origins throughout the text. He incorporates a hands-on approach to proofs and connects algebra and geometry to various applications. The text focuses on linear equations, polynomial equations, and quadratic forms. The first several chapters cover foundational topics, including the importance of proofs and properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solution of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra
Book Synopsis Introduction to Algebraic Geometry and Algebraic Groups by :
Download or read book Introduction to Algebraic Geometry and Algebraic Groups written by and published by Elsevier. This book was released on 1980-01-01 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Algebraic Geometry and Algebraic Groups
Book Synopsis An Introduction to Algebraic Topology by : Andrew H. Wallace
Download or read book An Introduction to Algebraic Topology written by Andrew H. Wallace and published by Courier Corporation. This book was released on 2007-02-27 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: Homology theory on algebraic varieties. New York: Pergamon Press, 1957.
Download or read book Ruled Varieties written by Gerd Fischer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ruled varieties are unions of a family of linear spaces. They are objects of algebraic geometry as well as differential geometry, especially if the ruling is developable. This book is an introduction to both aspects, the algebraic and differential one. Starting from very elementary facts, the necessary techniques are developed, especially concerning Grassmannians and fundamental forms in a version suitable for complex projective algebraic geometry. Finally, this leads to recent results on the classification of developable ruled varieties and facts about tangent and secant varieties. Compared to many other topics of algebraic geometry, this is an area easily accessible to a graduate course.
