Introduction to Plane Algebraic Curves PDF Download
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Author: Ernst Kunz
Publisher: Springer Science & Business Media
ISBN: 0817644431
Category : Mathematics
Languages : en
Pages : 286
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Book Description
* Employs proven conception of teaching topics in commutative algebra through a focus on their applications to algebraic geometry, a significant departure from other works on plane algebraic curves in which the topological-analytic aspects are stressed *Requires only a basic knowledge of algebra, with all necessary algebraic facts collected into several appendices * Studies algebraic curves over an algebraically closed field K and those of prime characteristic, which can be applied to coding theory and cryptography * Covers filtered algebras, the associated graded rings and Rees rings to deduce basic facts about intersection theory of plane curves, applications of which are standard tools of computer algebra * Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook
Author: Surendramohan Ganguli
Publisher:
ISBN:
Category : Curves, Algebraic
Languages : en
Pages : 426
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Book Description
Author: Ernst Kunz
Publisher: Springer Science & Business Media
ISBN: 0817644431
Category : Mathematics
Languages : en
Pages : 286
Get Book Here
Book Description
* Employs proven conception of teaching topics in commutative algebra through a focus on their applications to algebraic geometry, a significant departure from other works on plane algebraic curves in which the topological-analytic aspects are stressed *Requires only a basic knowledge of algebra, with all necessary algebraic facts collected into several appendices * Studies algebraic curves over an algebraically closed field K and those of prime characteristic, which can be applied to coding theory and cryptography * Covers filtered algebras, the associated graded rings and Rees rings to deduce basic facts about intersection theory of plane curves, applications of which are standard tools of computer algebra * Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook
Author: Surendramohan Ganguli
Publisher:
ISBN:
Category : Curves, Algebraic
Languages : en
Pages : 152
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Book Description
Author: David Eisenbud
Publisher: Princeton University Press
ISBN: 1400881927
Category : Mathematics
Languages : en
Pages : 180
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Book Description
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: Vladimir Igorevich Arnolʹd
Publisher: American Mathematical Soc.
ISBN: 0821803085
Category : Mathematics
Languages : en
Pages : 70
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Book Description
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: I. I. Artobolevskii
Publisher: Elsevier
ISBN: 1483152421
Category : Technology & Engineering
Languages : en
Pages : 295
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Book Description
Mechanisms for the Generation of Plane Curves focuses on the possibility of generating plane curves through kinematic linkages. The book first offers information on the basic theory of the generation of curves by mechanisms with higher pairs of the fourth class and fundamentals of the theory of the generation of curves using mechanisms with lower pairs of class V. Discussions focus on generation of curves by centrode and trajectory pairs; generation of curves with five-link and six-link kinematic chains; basic theorem for the mechanical generation of algebraic curves; and use of the properties of individual forms of transformation mechanisms. The text then examines mechanical generation of straight lines and circles and mechanical generation of ellipses, hyperbolas, and parabolas. The publication ponders on the mechanical generation of third degree curves and mechanical generation of curves of the fourth degree. Topics include mechanisms for generating curves of the focal type; mechanisms for generating special forms of curves; and mechanisms for the generation of the conchoids of the straight line and the circle. The text is a dependable reference for readers interested in the mechanisms involved in plane curves.
Author: Harold Hilton
Publisher:
ISBN:
Category : Curves, Algebraic
Languages : en
Pages : 416
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Book Description
Author: J. Dennis Lawrence
Publisher: Courier Corporation
ISBN: 0486167666
Category : Mathematics
Languages : en
Pages : 244
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Book Description
DIVOne of the most beautiful aspects of geometry. Information on general properties, derived curves, geometric and analytic properties of each curve. 89 illus. /div
Author: Ernst Kunz
Publisher: Springer Science & Business Media
ISBN: 0817644431
Category : Mathematics
Languages : en
Pages : 285
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Book Description
* Employs proven conception of teaching topics in commutative algebra through a focus on their applications to algebraic geometry, a significant departure from other works on plane algebraic curves in which the topological-analytic aspects are stressed *Requires only a basic knowledge of algebra, with all necessary algebraic facts collected into several appendices * Studies algebraic curves over an algebraically closed field K and those of prime characteristic, which can be applied to coding theory and cryptography * Covers filtered algebras, the associated graded rings and Rees rings to deduce basic facts about intersection theory of plane curves, applications of which are standard tools of computer algebra * Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook
Author: Gerd Fischer
Publisher: American Mathematical Soc.
ISBN: 0821821229
Category : Mathematics
Languages : en
Pages : 249
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Book Description
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.
