Curves And Singularities

Download or read book Curves and Singularities written by James William Bruce and published by Cambridge University Press. This book was released on 1992-11-26 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition is an invaluable textbook for anyone who would like an introduction to the modern theories of catastrophies and singularities.

Download or read book Curves and Singularities written by J. W. Bruce and published by Cambridge University Press. This book was released on 1984-05-24 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Singularities of Plane Curves written by Eduardo Casas-Alvero and published by Cambridge University Press. This book was released on 2000-08-31 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.

Download or read book Differential Geometry Of Curves And Surfaces With Singularities written by Masaaki Umehara and published by World Scientific. This book was released on 2021-11-29 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unique and highly accessible approach to singularity theory from the perspective of differential geometry of curves and surfaces. It is written by three leading experts on the interplay between two important fields — singularity theory and differential geometry.The book introduces singularities and their recognition theorems, and describes their applications to geometry and topology, restricting the objects of attention to singularities of plane curves and surfaces in the Euclidean 3-space. In particular, by presenting the singular curvature, which originated through research by the authors, the Gauss-Bonnet theorem for surfaces is generalized to those with singularities. The Gauss-Bonnet theorem is intrinsic in nature, that is, it is a theorem not only for surfaces but also for 2-dimensional Riemannian manifolds. The book also elucidates the notion of Riemannian manifolds with singularities.These topics, as well as elementary descriptions of proofs of the recognition theorems, cannot be found in other books. Explicit examples and models are provided in abundance, along with insightful explanations of the underlying theory as well. Numerous figures and exercise problems are given, becoming strong aids in developing an understanding of the material.Readers will gain from this text a unique introduction to the singularities of curves and surfaces from the viewpoint of differential geometry, and it will be a useful guide for students and researchers interested in this subject.

Download or read book Resolution of Curve and Surface Singularities in Characteristic Zero written by K. Kiyek and published by Springer Science & Business Media. This book was released on 2012-09-11 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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}.

Download or read book Introduction to Singularities and Deformations written by Gert-Martin Greuel and published by Springer Science & Business Media. This book was released on 2007-02-23 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory and the theory of plane curve singularities. It includes complete proofs.

Download or read book Singular Points of Plane Curves written by C. T. C. Wall and published by Cambridge University Press. This book was released on 2004-11-15 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description