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Algebraic Functions And Projective Curves
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Book Synopsis Algebraic Functions and Projective Curves by : David Goldschmidt
Download or read book Algebraic Functions and Projective Curves written by David Goldschmidt and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to algebraic functions and projective curves. It covers a wide range of material by dispensing with the machinery of algebraic geometry and proceeding directly via valuation theory to the main results on function fields. It also develops the theory of singular curves by studying maps to projective space, including topics such as Weierstrass points in characteristic p, and the Gorenstein relations for singularities of plane curves.
Book Synopsis Algebraic Functions and Projective Curves by : David Goldschmidt
Download or read book Algebraic Functions and Projective Curves written by David Goldschmidt and published by Springer Science & Business Media. This book was released on 2003 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of a set of notes for a series of lectures I orginally gave at the Center for Communications Research and then at Princeton University. The motivation was to try to understand the basic facts about algebraic curves without the modern prerequisite machinery of algebraic geometry. Of course, one might well ask if this is a good thing to do. There is no clear answer to this question. In short, we are trading off easier access to the facts against a loss of generality and an impaired understanding of some fundamental ideas. Whether or not this is a useful tradeoff is something you will have to decide for yourself. One of my objectives was to make the exposition as self-contained as possible. Given the choice between a reference and a proof, I usually chose the latter. - though I worked out many of these arguments myself, I think I can con?dently predict that few, if any, of them are novel. I also made an effort to cover some topics that seem to have been somewhat neglected in the expository literature.
Book Synopsis Algebraic Curves and One-Dimensional Fields by : Fedor Bogomolov
Download or read book Algebraic Curves and One-Dimensional Fields written by Fedor Bogomolov and published by American Mathematical Soc.. This book was released on 2002 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text covers the essential topics in the geometry of algebraic curves, such as line and vector bundles, the Riemann-Roch Theorem, divisors, coherent sheaves, and zeroth and first cohomology groups. It demonstrates how curves can act as a natural introduction to algebraic geometry.
Book Synopsis An Introduction to Algebraic Geometry by : Kenji Ueno
Download or read book An Introduction to Algebraic Geometry written by Kenji Ueno and published by American Mathematical Soc.. This book was released on 1997 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to algebraic geometry allows readers to grasp the fundamentals of the subject with only linear algebra and calculus as prerequisites. After a brief history of the subject, the book introduces projective spaces and projective varieties, and explains plane curves and resolution of their singularities. The volume further develops the geometry of algebraic curves and treats congruence zeta functions of algebraic curves over a finite field. It concludes with a complex analytical discussion of algebraic curves. The author emphasizes computation of concrete examples rather than proofs, and these examples are discussed from various viewpoints. This approach allows readers to develop a deeper understanding of the theorems.
Book Synopsis Introduction to Plane Algebraic Curves by : Ernst Kunz
Download or read book Introduction to Plane Algebraic Curves written by Ernst Kunz and published by Springer Science & Business Media. This book was released on 2007-06-10 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Employs proven conception of teaching topics in commutative algebra through a focus on their applications to algebraic geometry, a significant departure from other works on plane algebraic curves in which the topological-analytic aspects are stressed *Requires only a basic knowledge of algebra, with all necessary algebraic facts collected into several appendices * Studies algebraic curves over an algebraically closed field K and those of prime characteristic, which can be applied to coding theory and cryptography * Covers filtered algebras, the associated graded rings and Rees rings to deduce basic facts about intersection theory of plane curves, applications of which are standard tools of computer algebra * Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook
Book Synopsis Algebraic Curves and Riemann Surfaces by : Rick Miranda
Download or read book Algebraic Curves and Riemann Surfaces written by Rick Miranda and published by American Mathematical Soc.. This book was released on 1995 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking centre stage. But the main examples come fromprojective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Dualtiy Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves andcohomology are introduced as a unifying device in the later chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one term of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-term course in complex variables or a year-long course in algebraic geometry.
Book Synopsis Algebraic Functions and Projective Curves by : David M. Goldschmidt
Download or read book Algebraic Functions and Projective Curves written by David M. Goldschmidt and published by . This book was released on 2003 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic Curves by : Robert John Walker
Download or read book Algebraic Curves written by Robert John Walker and published by . This book was released on 1950 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Curves on an Algebraic Surface. (AM-59), Volume 59 by : David Mumford
Download or read book Lectures on Curves on an Algebraic Surface. (AM-59), Volume 59 written by David Mumford and published by Princeton University Press. This book was released on 2016-03-02 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint.
Book Synopsis Algebraic Curves over a Finite Field by : J. W. P. Hirschfeld
Download or read book Algebraic Curves over a Finite Field written by J. W. P. Hirschfeld and published by Princeton University Press. This book was released on 2013-03-25 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.
Book Synopsis Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable by : Rida T Farouki
Download or read book Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable written by Rida T Farouki and published by Springer Science & Business Media. This book was released on 2007-10-11 with total page 725 pages. Available in PDF, EPUB and Kindle. Book excerpt: By virtue of their special algebraic structures, Pythagorean-hodograph (PH) curves offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. This book offers a comprehensive and self-contained treatment of the mathematical theory of PH curves, including algorithms for their construction and examples of their practical applications. It emphasizes the interplay of ideas from algebra and geometry and their historical origins and includes many figures, worked examples, and detailed algorithm descriptions.
Book Synopsis Algebraic Curves and Finite Fields by : Harald Niederreiter
Download or read book Algebraic Curves and Finite Fields written by Harald Niederreiter and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-08-20 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra and number theory have always been counted among the most beautiful and fundamental mathematical areas with deep proofs and elegant results. However, for a long time they were not considered of any substantial importance for real-life applications. This has dramatically changed with the appearance of new topics such as modern cryptography, coding theory, and wireless communication. Nowadays we find applications of algebra and number theory frequently in our daily life. We mention security and error detection for internet banking, check digit systems and the bar code, GPS and radar systems, pricing options at a stock market, and noise suppression on mobile phones as most common examples. This book collects the results of the workshops "Applications of algebraic curves" and "Applications of finite fields" of the RICAM Special Semester 2013. These workshops brought together the most prominent researchers in the area of finite fields and their applications around the world. They address old and new problems on curves and other aspects of finite fields, with emphasis on their diverse applications to many areas of pure and applied mathematics.
Book Synopsis Algebraic Geometry And Its Applications: Dedicated To Gilles Lachaud On His 60th Birthday - Proceedings Of The First Saga Conference by : Robert Rolland
Download or read book Algebraic Geometry And Its Applications: Dedicated To Gilles Lachaud On His 60th Birthday - Proceedings Of The First Saga Conference written by Robert Rolland and published by World Scientific. This book was released on 2008-04-17 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers many topics, including number theory, Boolean functions, combinatorial geometry, and algorithms over finite fields. It contains many new, theoretical and applicable results, as well as surveys that were presented by the top specialists in these areas. New results include an answer to one of Serre's questions, posted in a letter to Top; cryptographic applications of the discrete logarithm problem related to elliptic curves and hyperelliptic curves; construction of function field towers; construction of new classes of Boolean cryptographic functions; and algorithmic applications of algebraic geometry.
Book Synopsis Capacity Theory on Algebraic Curves by : Robert S. Rumely
Download or read book Capacity Theory on Algebraic Curves written by Robert S. Rumely and published by Springer. This book was released on 2006-11-14 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: Capacity is a measure of size for sets, with diverse applications in potential theory, probability and number theory. This book lays foundations for a theory of capacity for adelic sets on algebraic curves. Its main result is an arithmetic one, a generalization of a theorem of Fekete and Szegö which gives a sharp existence/finiteness criterion for algebraic points whose conjugates lie near a specified set on a curve. The book brings out a deep connection between the classical Green's functions of analysis and Néron's local height pairings; it also points to an interpretation of capacity as a kind of intersection index in the framework of Arakelov Theory. It is a research monograph and will primarily be of interest to number theorists and algebraic geometers; because of applications of the theory, it may also be of interest to logicians. The theory presented generalizes one due to David Cantor for the projective line. As with most adelic theories, it has a local and a global part. Let /K be a smooth, complete curve over a global field; let Kv denote the algebraic closure of any completion of K. The book first develops capacity theory over local fields, defining analogues of the classical logarithmic capacity and Green's functions for sets in (Kv). It then develops a global theory, defining the capacity of a galois-stable set in (Kv) relative to an effictive global algebraic divisor. The main technical result is the construction of global algebraic functions whose logarithms closely approximate Green's functions at all places of K. These functions are used in proving the generalized Fekete-Szegö theorem; because of their mapping properties, they may be expected to have other applications as well.
Book Synopsis Algebraic Curves and Riemann Surfaces for Undergraduates by : Anil Nerode
Download or read book Algebraic Curves and Riemann Surfaces for Undergraduates written by Anil Nerode and published by Springer Nature. This book was released on 2023-01-16 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory relating algebraic curves and Riemann surfaces exhibits the unity of mathematics: topology, complex analysis, algebra and geometry all interact in a deep way. This textbook offers an elementary introduction to this beautiful theory for an undergraduate audience. At the heart of the subject is the theory of elliptic functions and elliptic curves. A complex torus (or “donut”) is both an abelian group and a Riemann surface. It is obtained by identifying points on the complex plane. At the same time, it can be viewed as a complex algebraic curve, with addition of points given by a geometric “chord-and-tangent” method. This book carefully develops all of the tools necessary to make sense of this isomorphism. The exposition is kept as elementary as possible and frequently draws on familiar notions in calculus and algebra to motivate new concepts. Based on a capstone course given to senior undergraduates, this book is intended as a textbook for courses at this level and includes a large number of class-tested exercises. The prerequisites for using the book are familiarity with abstract algebra, calculus and analysis, as covered in standard undergraduate courses.
Book Synopsis Algebraic Curves, the Brill and Noether Way by : Eduardo Casas-Alvero
Download or read book Algebraic Curves, the Brill and Noether Way written by Eduardo Casas-Alvero and published by Springer Nature. This book was released on 2019-11-30 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the central facts of the local, projective and intrinsic theories of complex algebraic plane curves, with complete proofs and starting from low-level prerequisites. It includes Puiseux series, branches, intersection multiplicity, Bézout theorem, rational functions, Riemann-Roch theorem and rational maps. It is aimed at graduate and advanced undergraduate students, and also at anyone interested in algebraic curves or in an introduction to algebraic geometry via curves.
Book Synopsis Algebraic Curves by : William Fulton
Download or read book Algebraic Curves written by William Fulton and published by . This book was released on 2008 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of these notes is to develop the theory of algebraic curves from the viewpoint of modern algebraic geometry, but without excessive prerequisites. We have assumed that the reader is familiar with some basic properties of rings, ideals and polynomials, such as is often covered in a one-semester course in modern algebra; additional commutative algebra is developed in later sections.
