Singularities Of Plane Curves
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Author | : Eduardo Casas-Alvero |
Publisher | : Cambridge University Press |
Total Pages | : 363 |
Release | : 2000-08-31 |
Genre | : Mathematics |
ISBN | : 0521789591 |
Download Singularities of Plane Curves Book in PDF, Epub and Kindle
Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.
Author | : C. T. C. Wall |
Publisher | : Cambridge University Press |
Total Pages | : 386 |
Release | : 2004-11-15 |
Genre | : Mathematics |
ISBN | : 9780521547741 |
Download Singular Points of Plane Curves Book in PDF, Epub and Kindle
Publisher Description
Author | : David Eisenbud |
Publisher | : Princeton University Press |
Total Pages | : 180 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 1400881927 |
Download Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM-110), Volume 110 Book in PDF, Epub and Kindle
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 | : James William Bruce |
Publisher | : Cambridge University Press |
Total Pages | : 344 |
Release | : 1992-11-26 |
Genre | : Mathematics |
ISBN | : 9780521429993 |
Download Curves and Singularities Book in PDF, Epub and Kindle
This second edition is an invaluable textbook for anyone who would like an introduction to the modern theories of catastrophies and singularities.
Author | : Gerd Fischer |
Publisher | : American Mathematical Soc. |
Total Pages | : 249 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0821821229 |
Download Plane Algebraic Curves Book in PDF, Epub and Kindle
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 | : Harold Hilton |
Publisher | : |
Total Pages | : 416 |
Release | : 1920 |
Genre | : Curves, Algebraic |
ISBN | : |
Download Plane Algebraic Curves Book in PDF, Epub and Kindle
Author | : Masaaki Umehara |
Publisher | : World Scientific |
Total Pages | : 387 |
Release | : 2021-11-29 |
Genre | : Mathematics |
ISBN | : 9811237158 |
Download Differential Geometry Of Curves And Surfaces With Singularities Book in PDF, Epub and Kindle
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 | : Vladimir Igorevich Arnolʹd |
Publisher | : American Mathematical Soc. |
Total Pages | : 70 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : 0821803085 |
Download Topological Invariants of Plane Curves and Caustics Book in PDF, Epub and Kindle
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 | : Eduardo Casas-Alvero |
Publisher | : |
Total Pages | : 363 |
Release | : 2014-05-14 |
Genre | : MATHEMATICS |
ISBN | : 9781107363113 |
Download Singularities of Plane Curves Book in PDF, Epub and Kindle
Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.
Author | : David Eisenbud |
Publisher | : Princeton University Press |
Total Pages | : 188 |
Release | : 1985 |
Genre | : Mathematics |
ISBN | : 9780691083810 |
Download Three-dimensional Link Theory and Invariants of Plane Curve Singularities Book in PDF, Epub and Kindle
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.