Singular Points of Plane Curves PDF Download
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Author: C. T. C. Wall
Publisher: Cambridge University Press
ISBN: 9780521547741
Category : Mathematics
Languages : en
Pages : 386
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Book Description
Publisher Description
Author: C. T. C. Wall
Publisher: Cambridge University Press
ISBN: 9780521547741
Category : Mathematics
Languages : en
Pages : 386
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Book Description
Publisher Description
Author:
Publisher:
ISBN: 9780511265372
Category : Curves, Plane
Languages : en
Pages : 370
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Book Description
The study of singularities uses techniques from algebra, algebraic geometry, complex analysis and topology. This book introduces graduate students to this attractive area of mathematics. It is based on a MSc course taught by the author and also is an original synthesis, with new views and results not found elsewhere.
Author: Eduardo Casas-Alvero
Publisher: Cambridge University Press
ISBN: 0521789591
Category : Mathematics
Languages : en
Pages : 363
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Book Description
Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.
Author: C. T. C. Wall
Publisher: Cambridge University Press
ISBN: 9780521839044
Category : Mathematics
Languages : en
Pages : 384
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Book Description
This book has arisen from the author's successful course at Liverpool University. The text covers all the essentials in a style that is detailed and expertly written by one of the foremost researchers and teachers working in the field. Ideal for either course use or independent study, the volume guides students through the key concepts that will enable them to move on to more detailed study or research within the field.
Author: Julian Lowell Coolidge
Publisher: Courier Corporation
ISBN: 9780486495767
Category : Mathematics
Languages : en
Pages : 554
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Book Description
A thorough introduction to the theory of algebraic plane curves and their relations to various fields of geometry and analysis. Almost entirely confined to the properties of the general curve, and chiefly employs algebraic procedure. Geometric methods are much employed, however, especially those involving the projective geometry of hyperspace. 1931 edition. 17 illustrations.
Author: Surendramohan Ganguli
Publisher:
ISBN:
Category : Curves, Algebraic
Languages : en
Pages : 422
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Book Description
Author: Gerd Fischer
Publisher: American Mathematical Soc.
ISBN: 0821821229
Category : Curves, Algebraic
Languages : en
Pages : 249
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Book Description
This is an excellent introduction to algebraic geometry, which assumes only standard undergraduate mathematical topics: complex analysis, rings and fields, and topology. Reading this book will help establish the geometric intuition that lies behind the more advanced ideas and techniques used in the study of higher-dimensional varieties.
Author: K. Kiyek
Publisher: Springer Science & Business Media
ISBN: 1402020295
Category : Mathematics
Languages : en
Pages : 506
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Book Description
The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. •• . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it • To solve the problem, it is enough to consider a special kind of Cremona trans formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.
Author: Ralph Howard Fowler
Publisher:
ISBN:
Category : Curves, Plane
Languages : en
Pages : 124
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Book Description
Author: Ernst Kunz
Publisher: Springer Science & Business Media
ISBN: 0817644431
Category : Mathematics
Languages : en
Pages : 286
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Book Description
* 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
