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Author : Eduardo Casas-Alvero
Publisher : Cambridge University Press
Page : 363 pages
File Size : 51,8 Mb
Release : 2000-08-31
Category : Mathematics
ISBN : 9780521789592
Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.
Author : C. T. C. Wall
Publisher : Cambridge University Press
Page : 386 pages
File Size : 48,6 Mb
Release : 2004-11-15
Category : Mathematics
ISBN : 0521547741
Publisher Description
Author : David Eisenbud,Walter D. Neumann
Publisher : Princeton University Press
Page : 180 pages
File Size : 44,8 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881925
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.
Author : David Eisenbud,Walter D. Neumann
Publisher : Princeton University Press
Page : 188 pages
File Size : 45,5 Mb
Release : 1985
Category : Mathematics
ISBN : 0691083819
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.
Author : K. Kiyek,J.L. Vicente
Publisher : Springer Science & Business Media
Page : 506 pages
File Size : 44,8 Mb
Release : 2012-09-11
Category : Mathematics
ISBN : 9781402020292
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 : Eduardo Casas-Alvero
Publisher : Unknown
Page : 363 pages
File Size : 49,8 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 110736311X
Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.
Author : James William Bruce,P. J. Giblin
Publisher : Cambridge University Press
Page : 344 pages
File Size : 41,6 Mb
Release : 1992-11-26
Category : Mathematics
ISBN : 0521429994
This second edition is an invaluable textbook for anyone who would like an introduction to the modern theories of catastrophies and singularities.
Author : Masaaki Umehara,Kentaro Saji,Kotaro Yamada
Publisher : World Scientific
Page : 387 pages
File Size : 44,7 Mb
Release : 2021-11-29
Category : Mathematics
ISBN : 9789811237157
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.
Author : Anonim
Publisher : Unknown
Page : 370 pages
File Size : 49,6 Mb
Release : 2004
Category : Curves, Plane
ISBN : 0511265379
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 : Harold Hilton
Publisher : Unknown
Page : 416 pages
File Size : 50,7 Mb
Release : 1920
Category : Curves, Algebraic
ISBN : UCAL:$B526568
Author : Gert-Martin Greuel,Christoph Lossen,Eugenii I. Shustin
Publisher : Springer Science & Business Media
Page : 482 pages
File Size : 48,7 Mb
Release : 2007-02-23
Category : Mathematics
ISBN : 9783540284192
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.
Author : Gerd Fischer
Publisher : American Mathematical Soc.
Page : 249 pages
File Size : 55,9 Mb
Release : 2001
Category : Curves, Algebraic
ISBN : 9780821821220
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 : BRIESKORN,KNÖRRER
Publisher : Birkhäuser
Page : 730 pages
File Size : 53,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783034850971
Author : Vladimir Igorevich Arnolʹd
Publisher : American Mathematical Soc.
Page : 60 pages
File Size : 48,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821803080
This book describes recent progress in the topological study of plane curves. The theory of plane curves is much richer than knot theory, which may be considered the commutative version of the theory of plane curves. This study is based on singularity theory: the infinite-dimensional space of curves is subdivided by the discriminant hypersurfaces into parts consisting of generic curves of the same type. The invariants distinguishing the types are defined by their jumps at the crossings of these hypersurfaces. Arnold describes applications to the geometry of caustics and of wavefronts in symplectic and contact geometry. These applications extend the classical four-vertex theorem of elementary plane geometry to estimates on the minimal number of cusps necessary for the reversion of a wavefront and to generalizations of the last geometrical theorem of Jacobi on conjugated points on convex surfaces. These estimates open a new chapter in symplectic and contact topology: the theory of Lagrangian and Legendrian collapses, providing an unusual and far-reaching higher-dimensional extension of Sturm theory of the oscillations of linear combinations of eigenfunctions.
Author : Keith Kendig
Publisher : MAA
Page : 211 pages
File Size : 52,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9780883853535
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.
