Algebraic Curves And Their Applications

Algebraic Curves And Their Applications Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Algebraic Curves And Their Applications book. This book definitely worth reading, it is an incredibly well-written.

Algebraic Curves and Their Applications

Lubjana Beshaj,Tony Shaska
Algebraic Curves and Their Applications Book PDF

Author : Lubjana Beshaj,Tony Shaska
Publisher : American Mathematical Soc.
Page : 344 pages
File Size : 50,7 Mb
Release : 2019-02-26
Category : Curves, Algebraic
ISBN : 9781470442477

Get Book

Algebraic Curves and Their Applications by Lubjana Beshaj,Tony Shaska Pdf

This volume contains a collection of papers on algebraic curves and their applications. While algebraic curves traditionally have provided a path toward modern algebraic geometry, they also provide many applications in number theory, computer security and cryptography, coding theory, differential equations, and more. Papers cover topics such as the rational torsion points of elliptic curves, arithmetic statistics in the moduli space of curves, combinatorial descriptions of semistable hyperelliptic curves over local fields, heights on weighted projective spaces, automorphism groups of curves, hyperelliptic curves, dessins d'enfants, applications to Painlevé equations, descent on real algebraic varieties, quadratic residue codes based on hyperelliptic curves, and Abelian varieties and cryptography. This book will be a valuable resource for people interested in algebraic curves and their connections to other branches of mathematics.

Introduction to Plane Algebraic Curves

Ernst Kunz
Introduction to Plane Algebraic Curves Book PDF

Author : Ernst Kunz
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 52,8 Mb
Release : 2007-06-10
Category : Mathematics
ISBN : 9780817644437

Get Book

Introduction to Plane Algebraic Curves by Ernst Kunz Pdf

* 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

Singular Algebraic Curves

Gert-Martin Greuel,Christoph Lossen,Eugenii Shustin
Singular Algebraic Curves Book PDF

Author : Gert-Martin Greuel,Christoph Lossen,Eugenii Shustin
Publisher : Springer
Page : 553 pages
File Size : 41,9 Mb
Release : 2018-12-30
Category : Mathematics
ISBN : 9783030033507

Get Book

Singular Algebraic Curves by Gert-Martin Greuel,Christoph Lossen,Eugenii Shustin Pdf

Singular algebraic curves have been in the focus of study in algebraic geometry from the very beginning, and till now remain a subject of an active research related to many modern developments in algebraic geometry, symplectic geometry, and tropical geometry. The monograph suggests a unified approach to the geometry of singular algebraic curves on algebraic surfaces and their families, which applies to arbitrary singularities, allows one to treat all main questions concerning the geometry of equisingular families of curves, and, finally, leads to results which can be viewed as the best possible in a reasonable sense. Various methods of the cohomology vanishing theory as well as the patchworking construction with its modifications will be of a special interest for experts in algebraic geometry and singularity theory. The introductory chapters on zero-dimensional schemes and global deformation theory can well serve as a material for special courses and seminars for graduate and post-graduate students.Geometry in general plays a leading role in modern mathematics, and algebraic geometry is the most advanced area of research in geometry. In turn, algebraic curves for more than one century have been the central subject of algebraic geometry both in fundamental theoretic questions and in applications to other fields of mathematics and mathematical physics. Particularly, the local and global study of singular algebraic curves involves a variety of methods and deep ideas from geometry, analysis, algebra, combinatorics and suggests a number of hard classical and newly appeared problems which inspire further development in this research area.

Algebraic Curves and Finite Fields

Harald Niederreiter,Alina Ostafe,Daniel Panario,Arne Winterhof
Algebraic Curves and Finite Fields Book PDF

Author : Harald Niederreiter,Alina Ostafe,Daniel Panario,Arne Winterhof
Publisher : Walter de Gruyter GmbH & Co KG
Page : 254 pages
File Size : 55,6 Mb
Release : 2014-08-20
Category : Mathematics
ISBN : 9783110317916

Get Book

Algebraic Curves and Finite Fields by Harald Niederreiter,Alina Ostafe,Daniel Panario,Arne Winterhof Pdf

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.

Geometry of Curves

J.W. Rutter
Geometry of Curves Book PDF

Author : J.W. Rutter
Publisher : CRC Press
Page : 381 pages
File Size : 45,7 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9781482285673

Get Book

Geometry of Curves by J.W. Rutter Pdf

Interest in the study of geometry is currently enjoying a resurgence-understandably so, as the study of curves was once the playground of some very great mathematicians. However, many of the subject's more exciting aspects require a somewhat advanced mathematics background. For the "fun stuff" to be accessible, we need to offer students an introduction with modest prerequisites, one that stimulates their interest and focuses on problem solving. Integrating parametric, algebraic, and projective curves into a single text, Geometry of Curves offers students a unique approach that provides a mathematical structure for solving problems, not just a catalog of theorems. The author begins with the basics, then takes students on a fascinating journey from conics, higher algebraic and transcendental curves, through the properties of parametric curves, the classification of limaçons, envelopes, and finally to projective curves, their relationship to algebraic curves, and their application to asymptotes and boundedness. The uniqueness of this treatment lies in its integration of the different types of curves, its use of analytic methods, and its generous number of examples, exercises, and illustrations. The result is a practical text, almost entirely self-contained, that not only imparts a deeper understanding of the theory, but inspires a heightened appreciation of geometry and interest in more advanced studies.

Algebraic Curves over a Finite Field

J. W. P. Hirschfeld,Gabor Korchmaros,Fernando Torres
Algebraic Curves over a Finite Field Book PDF

Author : J. W. P. Hirschfeld,Gabor Korchmaros,Fernando Torres
Publisher : Princeton University Press
Page : 717 pages
File Size : 50,8 Mb
Release : 2013-03-25
Category : Mathematics
ISBN : 9781400847419

Get Book

Algebraic Curves over a Finite Field by J. W. P. Hirschfeld,Gabor Korchmaros,Fernando Torres Pdf

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.

Vertex Algebras and Algebraic Curves

Edward Frenkel,David Ben-Zvi
Vertex Algebras and Algebraic Curves Book PDF

Author : Edward Frenkel,David Ben-Zvi
Publisher : American Mathematical Soc.
Page : 418 pages
File Size : 42,8 Mb
Release : 2004-08-25
Category : Mathematics
ISBN : 9780821836743

Get Book

Vertex Algebras and Algebraic Curves by Edward Frenkel,David Ben-Zvi Pdf

Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book contains many original results, introduces important new concepts, and brings new insights into the theory of vertex algebras. The authors have made a great effort to make the book self-contained and accessible to readers of all backgrounds. Reviewers of the first edition anticipated that it would have a long-lasting influence on this exciting field of mathematics and would be very useful for graduate students and researchers interested in the subject. This second edition, substantially improved and expanded, includes several new topics, in particular an introduction to the Beilinson-Drinfeld theory of factorization algebras and the geometric Langlands correspondence.

Algebraic Curves in Cryptography

San Ling,Huaxiong Wang,Chaoping Xing
Algebraic Curves in Cryptography Book PDF

Author : San Ling,Huaxiong Wang,Chaoping Xing
Publisher : CRC Press
Page : 340 pages
File Size : 50,6 Mb
Release : 2013-06-13
Category : Computers
ISBN : 9781420079470

Get Book

Algebraic Curves in Cryptography by San Ling,Huaxiong Wang,Chaoping Xing Pdf

The reach of algebraic curves in cryptography goes far beyond elliptic curve or public key cryptography yet these other application areas have not been systematically covered in the literature. Addressing this gap, Algebraic Curves in Cryptography explores the rich uses of algebraic curves in a range of cryptographic applications, such as secret sh

Advances on Superelliptic Curves and Their Applications

L. Beshaj,T. Shaska,E. Zhupa
Advances on Superelliptic Curves and Their Applications Book PDF

Author : L. Beshaj,T. Shaska,E. Zhupa
Publisher : IOS Press
Page : 387 pages
File Size : 47,8 Mb
Release : 2015-07-16
Category : Computers
ISBN : 9781614995203

Get Book

Advances on Superelliptic Curves and Their Applications by L. Beshaj,T. Shaska,E. Zhupa Pdf

This book had its origins in the NATO Advanced Study Institute (ASI) held in Ohrid, Macedonia, in 2014. The focus of this ASI was the arithmetic of superelliptic curves and their application in different scientific areas, including whether all the applications of hyperelliptic curves, such as cryptography, mathematical physics, quantum computation and diophantine geometry, can be carried over to the superelliptic curves. Additional papers have been added which provide some background for readers who were not at the conference, with the intention of making the book logically more complete and easier to read, but familiarity with the basic facts of algebraic geometry, commutative algebra and number theory are assumed. The book is divided into three sections. The first part deals with superelliptic curves with regard to complex numbers, the automorphisms group and the corresponding Hurwitz loci. The second part of the book focuses on the arithmetic of the subject, while the third addresses some of the applications of superelliptic curves.

Codes and Algebraic Curves

Oliver Pretzel
Codes and Algebraic Curves Book PDF

Author : Oliver Pretzel
Publisher : Clarendon Press
Page : 209 pages
File Size : 43,6 Mb
Release : 1998-01-08
Category : Mathematics
ISBN : 9780191589041

Get Book

Codes and Algebraic Curves by Oliver Pretzel Pdf

The geometry of curves has fascinated mathematicians for 2500 years, and the theory has become highly abstract. Recently links have been made with the subject of error correction, leading to the creation of geometric Goppa codes, a new and important area of coding theory. This book is an updated and extended version of the last part of the successful book Error-Correcting Codes and Finite Fields. It provides an elementary introduction to Goppa codes, and includes many examples, calculations, and applications. The book is in two parts with an emphasis on motivation, and applications of the theory take precedence over proofs of theorems. The formal theory is, however, provided in the second part of the book, and several of the concepts and proofs have been simplified without sacrificing rigour.

Algebraic Curves

William Fulton
Algebraic Curves Book PDF

Author : William Fulton
Publisher : Unknown
Page : 120 pages
File Size : 52,8 Mb
Release : 2008
Category : Mathematics
ISBN : OCLC:1000336205

Get Book

Algebraic Curves by William Fulton Pdf

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.

Algebraic Geometry and Arithmetic Curves

Qing Liu,Reinie Erne
Algebraic Geometry and Arithmetic Curves Book PDF

Author : Qing Liu,Reinie Erne
Publisher : Oxford University Press
Page : 593 pages
File Size : 41,6 Mb
Release : 2006-06-29
Category : Mathematics
ISBN : 9780191547805

Get Book

Algebraic Geometry and Arithmetic Curves by Qing Liu,Reinie Erne Pdf

This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the funadmental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.

Algebraic Curves and Riemann Surfaces

Rick Miranda
Algebraic Curves and Riemann Surfaces Book PDF

Author : Rick Miranda
Publisher : American Mathematical Soc.
Page : 390 pages
File Size : 50,6 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821802687

Get Book

Algebraic Curves and Riemann Surfaces by Rick Miranda Pdf

The book was easy to understand, with many examples. The exercises were well chosen, and served to give further examples and developments of the theory. --William Goldman, University of Maryland 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 center stage. But the main examples come from projective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Duality 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 and cohomology are introduced as a unifying device in the latter chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one semester of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-semester course in complex variables or a year-long course in algebraic geometry.

The Advanced Geometry of Plane Curves and Their Applications

C. Zwikker
The Advanced Geometry of Plane Curves and Their Applications Book PDF

Author : C. Zwikker
Publisher : Courier Corporation
Page : 316 pages
File Size : 53,9 Mb
Release : 2011-11-30
Category : Mathematics
ISBN : 9780486153438

Get Book

The Advanced Geometry of Plane Curves and Their Applications by C. Zwikker Pdf

"Of chief interest to mathematicians, but physicists and others will be fascinated ... and intrigued by the fruitful use of non-Cartesian methods. Students ... should find the book stimulating." — British Journal of Applied Physics This study of many important curves, their geometrical properties, and their applications features material not customarily treated in texts on synthetic or analytic Euclidean geometry. Its wide coverage, which includes both algebraic and transcendental curves, extends to unusual properties of familiar curves along with the nature of lesser known curves. Informative discussions of the line, circle, parabola, ellipse, and hyperbola presuppose only the most elementary facts. The less common curves — cissoid, strophoid, spirals, the leminscate, cycloid, epicycloid, cardioid, and many others — receive introductions that explain both their basic and advanced properties. Derived curves-the involute, evolute, pedal curve, envelope, and orthogonal trajectories-are also examined, with definitions of their important applications. These range through the fields of optics, electric circuit design, hydraulics, hydrodynamics, classical mechanics, electromagnetism, crystallography, gear design, road engineering, orbits of subatomic particles, and similar areas in physics and engineering. The author represents the points of the curves by complex numbers, rather than the real Cartesian coordinates, an approach that permits simple, direct, and elegant proofs.

Capacity Theory on Algebraic Curves

Robert S. Rumely
Capacity Theory on Algebraic Curves Book PDF

Author : Robert S. Rumely
Publisher : Lecture Notes in Mathematics
Page : 452 pages
File Size : 53,9 Mb
Release : 1989-07-05
Category : Mathematics
ISBN : CORNELL:31924050976053

Get Book

Capacity Theory on Algebraic Curves by Robert S. Rumely Pdf

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.