Singular Points of Plane Curves PDF Download

Author: C. T. C. Wall
Publisher: Cambridge University Press
ISBN: 9780521547741
Category : Mathematics
Languages : en
Pages : 386

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Author: Eduardo Casas-Alvero
Publisher: Cambridge University Press
ISBN: 0521789591
Category : Mathematics
Languages : en
Pages : 363

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Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.

Author:
Publisher:
ISBN: 9780511265372
Category : Curves, Plane
Languages : en
Pages : 370

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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: Surendramohan Ganguli
Publisher:
ISBN:
Category : Curves, Algebraic
Languages : en
Pages : 422

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Author: Julian Lowell Coolidge
Publisher: Courier Corporation
ISBN: 9780486495767
Category : Mathematics
Languages : en
Pages : 554

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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: C. T. C. Wall
Publisher: Cambridge University Press
ISBN: 9780521839044
Category : Mathematics
Languages : en
Pages : 384

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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: Dmitry Kerner
Publisher:
ISBN:
Category :
Languages : en
Pages : 13

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Author: Esther Eleanor Benedict
Publisher:
ISBN:
Category : Curves, Plane
Languages : en
Pages : 120

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Author: Ralph Howard Fowler
Publisher:
ISBN:
Category : Curves, Plane
Languages : en
Pages : 132

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Author: K. Kiyek
Publisher: Springer Science & Business Media
ISBN: 1402020295
Category : Mathematics
Languages : en
Pages : 506

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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}.