topology of algebraic curves

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Topology Of Algebraic Curves

Author : Alex Degtyarev
ISBN : 9783110258424
Genre : Mathematics
File Size : 87. 99 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 singularplane 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 : 73. 17 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.

Topology Of Algebraic Varieties And Singularities

Author : Anatoly Libgober
ISBN : 9780821848906
Genre : Mathematics
File Size : 21. 18 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.

A Topological Study Of Certain Plane Algebraic Curves

Author : Lucy Elizabeth Berger
ISBN : CORNELL:31924001149099
Genre : Mathematics
File Size : 25. 83 MB
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A Guide To Plane Algebraic Curves

Author : Keith Kendig
ISBN : 9780883853535
Genre : Mathematics
File Size : 67. 59 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.

Algebraic Curves And Riemann Surfaces

Author : Rick Miranda
ISBN : 9780821802687
Genre : Mathematics
File Size : 43. 60 MB
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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.

Topology Of Real Algebraic Varieties And Related Topics

Author : V. Kharlamov
ISBN : 082180555X
Genre : Mathematics
File Size : 59. 57 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).

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