topology of algebraic curves

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Topology Of Algebraic Curves

Author : Alex Degtyarev
ISBN : 9783110258424
Genre : Mathematics
File Size : 47. 75 MB
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The book summarizes the state and new results on the topology of trigonal curves in geometrically ruled surfaces. Emphasis is placed upon various applications of the theory to related areas, most notably singular plane curves of small degree, elliptic surfaces, and Lefschetz fibrations (both complex and real), and Hurwitz equivalence of braid monodromy factorizations. The monograph conveys recent knowledge about related objects and is of interest to researchers and graduate students in the fields of topology and of complex and real algebraic varieties.

Complex Algebraic Curves

Author : Frances Clare Kirwan
ISBN : 0521423538
Genre : Mathematics
File Size : 76. 74 MB
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This development of the theory of complex algebraic curves was one of the peaks of nineteenth century mathematics. They have many fascinating properties and arise in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.

A Topological Study Of Certain Plane Algebraic Curves

Author : Lucy Elizabeth Berger
ISBN : CORNELL:31924001149099
Genre : Mathematics
File Size : 83. 56 MB
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Introduction To Plane Algebraic Curves

Author : Ernst Kunz
ISBN : 9780817644437
Genre : Mathematics
File Size : 70. 83 MB
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* 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

Topology Of Algebraic Varieties And Singularities

Author : Anatoly Libgober
ISBN : 9780821848906
Genre : Mathematics
File Size : 81. 12 MB
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This volume contains invited expository and research papers from the conference Topology of Algebraic Varieties, in honor of Anatoly Libgober's 60th birthday, held June 22-26, 2009, in Jaca, Spain. The volume contains four parts corresponding to the four main focal points of the conference: algebraic geometry and fundamental groups, braids and knots, hyperplane arrangements, and singularities. Together, the papers provide an overview of the current status of a broad range of topological questions in Algebraic Geometry.

Topology Of Real Algebraic Varieties And Related Topics

Author : V. Kharlamov
ISBN : 082180555X
Genre : Mathematics
File Size : 83. 7 MB
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This volume is dedicated to the memory of the Russian mathematician D. A. Gudkov. It contains papers written by his friends, students, and collaborators and is devoted mainly to the areas where Gudkov made important contributions. Several papers include new results on the topology of real plane algebraic curves (the Hilbert 16th problem).

A Guide To Plane Algebraic Curves

Author : Keith Kendig
ISBN : 9780883853535
Genre : Mathematics
File Size : 43. 84 MB
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This Guide is a friendly introduction to plane algebraic curves. It emphasizes geometry and intuition, and the presentation is kept concrete. You'll find an abundance of pictures and examples to help develop your intuition about the subject, which is so basic to understanding and asking fruitful questions. Highlights of the elementary theory are covered, which for some could be an end in itself, and for others an invitation to investigate further. Proofs, when given, are mostly sketched, some in more detail, but typically with less. References to texts that provide further discussion are often included. Computer algebra software has made getting around in algebraic geometry much easier. Algebraic curves and geometry are now being applied to areas such as cryptography, complexity and coding theory, robotics, biological networks, and coupled dynamical systems. Algebraic curves were used in Andrew Wiles' proof of Fermat's Last Theorem, and to understand string theory, you need to know some algebraic geometry. There are other areas on the horizon for which the concepts and tools of algebraic curves and geometry hold tantalizing promise. This introduction to algebraic curves will be appropriate for a wide segment of scientists and engineers wanting an entrance to this burgeoning subject.

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