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 Book excerpt: Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.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 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
Download or read book Three Dimensional Link Theory and Invariants of Plane Curve Singularities AM 110 Volume 110 written by David Eisenbud and published by Princeton University Press. This book was released on 2016-03-02 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a new foundation for the theory of links in 3-space modeled on the modern developmentby Jaco, Shalen, Johannson, Thurston et al. of the theory of 3-manifolds. The basic construction is a method of obtaining any link by "splicing" links of the simplest kinds, namely those whose exteriors are Seifert fibered or hyperbolic. This approach to link theory is particularly attractive since most invariants of links are additive under splicing. Specially distinguished from this viewpoint is the class of links, none of whose splice components is hyperbolic. It includes all links constructed by cabling and connected sums, in particular all links of singularities of complex plane curves. One of the main contributions of this monograph is the calculation of invariants of these classes of links, such as the Alexander polynomials, monodromy, and Seifert forms.
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 Plane Algebraic Curves written by Harold Hilton and published by . This book was released on 1920 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Plane Algebraic Curves written by Gerd Fischer and published by American Mathematical Soc.. This book was released on 2001 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Singularities of Plane Curves written by Eduardo Casas-Alvero and published by . This book was released on 2014-05-14 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 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 The Theory of Plane Curves written by Surendramohan Ganguli and published by . This book was released on 1925 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Three dimensional Link Theory and Invariants of Plane Curve Singularities written by David Eisenbud and published by Princeton University Press. This book was released on 1985 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a new foundation for the theory of links in 3-space modeled on the modern developmentby Jaco, Shalen, Johannson, Thurston et al. of the theory of 3-manifolds. The basic construction is a method of obtaining any link by "splicing" links of the simplest kinds, namely those whose exteriors are Seifert fibered or hyperbolic. This approach to link theory is particularly attractive since most invariants of links are additive under splicing. Specially distinguished from this viewpoint is the class of links, none of whose splice components is hyperbolic. It includes all links constructed by cabling and connected sums, in particular all links of singularities of complex plane curves. One of the main contributions of this monograph is the calculation of invariants of these classes of links, such as the Alexander polynomials, monodromy, and Seifert forms.
Download or read book A Guide to Plane Algebraic Curves written by Keith Kendig and published by MAA. This book was released on 2011 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to the plane algebraic curves that also serves as a natural entry point to algebraic geometry. This book can be used for an undergraduate course, or as a companion to algebraic geometry at graduate level.
Download or read book Plane Curves of the Eighth Order written by Elizabeth Buchanan Cowley and published by . This book was released on 1908 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Efficient Resolution of Singularities of Plane Curves written by Dexter Kozen and published by . This book was released on 1994 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Topological Invariants of Plane Curves and Caustics written by Vladimir Igorevich Arnolʹd and published by American Mathematical Soc.. This book was released on with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is the first exposition of a new theory which unifies the theories of knots, plane curves, caustics, and wavefronts in differential, symplectic, and contact geometry and topology.
Download or read book A Treatise on Algebraic Plane Curves written by Julian Lowell Coolidge and published by Courier Dover Publications. This book was released on 1931 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental properties of polynomials. Elementary properties of curves. Real curves. Real circuits of curves. Elementary invariant theory. Projective theory of singular points. Plucker's equations, and klein's equations. Covariant curves. Metrical properties of curves. The singular points. The reduction of singularities. Development in series. Clustering singularities. Adjoint curves and plucker's equations. Systems of points on a curve. Abelian integrals. Singular points of correspondences. Moduli and limiting values. Curves of special type. Non-linear series of groups of points on a curve. Higher theory of correspondences. Parametric representation of the general curve. A shetch. Rational curves. Postulation of linear systems by points.
