Pencils Of Cubics And Algebraic Curves In The Real Projective Plane

Author : Séverine Fiedler - Le Touzé
Publisher : CRC Press
Page : 238 pages
File Size : 48,8 Mb
Release : 2018-12-07
Category : Mathematics
ISBN : 9780429838248

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Pencils of Cubics and Algebraic Curves in the Real Projective Plane by Séverine Fiedler - Le Touzé Pdf

Pencils of Cubics and Algebraic Curves in the Real Projective Plane thoroughly examines the combinatorial configurations of n generic points in RP2. Especially how it is the data describing the mutual position of each point with respect to lines and conics passing through others. The first section in this book answers questions such as, can one count the combinatorial configurations up to the action of the symmetric group? How are they pairwise connected via almost generic configurations? These questions are addressed using rational cubics and pencils of cubics for n = 6 and 7. The book’s second section deals with configurations of eight points in the convex position. Both the combinatorial configurations and combinatorial pencils are classified up to the action of the dihedral group D8. Finally, the third section contains plentiful applications and results around Hilbert’s sixteenth problem. The author meticulously wrote this book based upon years of research devoted to the topic. The book is particularly useful for researchers and graduate students interested in topology, algebraic geometry and combinatorics. Features: Examines how the shape of pencils depends on the corresponding configurations of points Includes topology of real algebraic curves Contains numerous applications and results around Hilbert’s sixteenth problem About the Author: Séverine Fiedler-le Touzé has published several papers on this topic and has been invited to present at many conferences. She holds a Ph.D. from University Rennes1 and was a post-doc at the Mathematical Sciences Research Institute in Berkeley, California.

Author : Séverine Fiedler - Le Touzé
Publisher : CRC Press
Page : 226 pages
File Size : 46,7 Mb
Release : 2018-12-07
Category : Mathematics
ISBN : 9780429838255

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Pencils of Cubics and Algebraic Curves in the Real Projective Plane by Séverine Fiedler - Le Touzé Pdf

Pencils of Cubics and Algebraic Curves in the Real Projective Plane thoroughly examines the combinatorial configurations of n generic points in RP2. Especially how it is the data describing the mutual position of each point with respect to lines and conics passing through others. The first section in this book answers questions such as, can one count the combinatorial configurations up to the action of the symmetric group? How are they pairwise connected via almost generic configurations? These questions are addressed using rational cubics and pencils of cubics for n = 6 and 7. The book’s second section deals with configurations of eight points in the convex position. Both the combinatorial configurations and combinatorial pencils are classified up to the action of the dihedral group D8. Finally, the third section contains plentiful applications and results around Hilbert’s sixteenth problem. The author meticulously wrote this book based upon years of research devoted to the topic. The book is particularly useful for researchers and graduate students interested in topology, algebraic geometry and combinatorics. Features: Examines how the shape of pencils depends on the corresponding configurations of points Includes topology of real algebraic curves Contains numerous applications and results around Hilbert’s sixteenth problem About the Author: Séverine Fiedler-le Touzé has published several papers on this topic and has been invited to present at many conferences. She holds a Ph.D. from University Rennes1 and was a post-doc at the Mathematical Sciences Research Institute in Berkeley, California.

Author : Gerd Fischer
Publisher : American Mathematical Soc.
Page : 249 pages
File Size : 45,5 Mb
Release : 2001
Category : Curves, Algebraic
ISBN : 9780821821220

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Plane Algebraic Curves by Gerd Fischer Pdf

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 : Christopher G. Gibson
Publisher : Cambridge University Press
Page : 278 pages
File Size : 52,6 Mb
Release : 1998-11-26
Category : Mathematics
ISBN : 0521641403

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Elementary Geometry of Algebraic Curves by Christopher G. Gibson Pdf

Here is an introduction to plane algebraic curves from a geometric viewpoint, designed as a first text for undergraduates in mathematics, or for postgraduate and research workers in the engineering and physical sciences. The book is well illustrated and contains several hundred worked examples and exercises. From the familiar lines and conics of elementary geometry the reader proceeds to general curves in the real affine plane, with excursions to more general fields to illustrate applications, such as number theory. By adding points at infinity the affine plane is extended to the projective plane, yielding a natural setting for curves and providing a flood of illumination into the underlying geometry. A minimal amount of algebra leads to the famous theorem of Bezout, while the ideas of linear systems are used to discuss the classical group structure on the cubic.

Author : Robert Bix
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 41,5 Mb
Release : 2006-07-24
Category : Mathematics
ISBN : 9780387318028

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Conics and Cubics by Robert Bix Pdf

Conics and Cubics offers an accessible and well illustrated introduction to algebraic curves. By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout’s Theorem on the number of intersections of two curves. The subject area is described by means of concrete and accessible examples. The book is a text for a one-semester course.

Author : Harold Hilton
Publisher : Unknown
Page : 416 pages
File Size : 42,8 Mb
Release : 1932
Category : Curves
ISBN : UCAL:B4248693

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Plane Algebraic Curves by Harold Hilton Pdf

Author : Keith Kendig
Publisher : MAA
Page : 211 pages
File Size : 55,9 Mb
Release : 2011
Category : Mathematics
ISBN : 9780883853535

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A Guide to Plane Algebraic Curves by Keith Kendig Pdf

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.

Author : Maxim E. Kazaryan,Sergei K. Lando,Victor V. Prasolov
Publisher : Springer
Page : 231 pages
File Size : 48,6 Mb
Release : 2019-01-21
Category : Mathematics
ISBN : 9783030029432

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Algebraic Curves by Maxim E. Kazaryan,Sergei K. Lando,Victor V. Prasolov Pdf

This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well. The book begins by studying individual smooth algebraic curves, including the most beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces. The book does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass points – are treated at a basic level that does not require a profound command of algebraic geometry, but which is sufficient for extending them to vector bundles and other geometric objects associated to moduli spaces. Nevertheless, it offers clear information on the construction of the moduli spaces, and provides readers with tools for practical operations with this notion. Based on several lecture courses given by the authors at the Independent University of Moscow and Higher School of Economics, the book also includes a wealth of problems, making it suitable not only for individual research, but also as a textbook for undergraduate and graduate coursework

Author : Edoardo Ballico,Ciro Ciliberto
Publisher : Springer
Page : 293 pages
File Size : 40,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540481881

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Algebraic Curves and Projective Geometry by Edoardo Ballico,Ciro Ciliberto Pdf

Author : Robert J. Walker
Publisher : Unknown
Page : 228 pages
File Size : 49,7 Mb
Release : 1950
Category : Electronic
ISBN : 8210379456XXX

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Algebraic Curves by Robert J. Walker Pdf

Author : Rida T Farouki
Publisher : Springer Science & Business Media
Page : 725 pages
File Size : 51,6 Mb
Release : 2008-02-01
Category : Mathematics
ISBN : 9783540733980

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Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable by Rida T Farouki Pdf

By virtue of their special algebraic structures, Pythagorean-hodograph (PH) curves offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. This book offers a comprehensive and self-contained treatment of the mathematical theory of PH curves, including algorithms for their construction and examples of their practical applications. It emphasizes the interplay of ideas from algebra and geometry and their historical origins and includes many figures, worked examples, and detailed algorithm descriptions.

Author : H.S.M. Coxeter
Publisher : Springer Science & Business Media
Page : 236 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461227342

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The Real Projective Plane by H.S.M. Coxeter Pdf

Along with many small improvements, this revised edition contains van Yzeren's new proof of Pascal's theorem (§1.7) and, in Chapter 2, an improved treatment of order and sense. The Sylvester-Gallai theorem, instead of being introduced as a curiosity, is now used as an essential step in the theory of harmonic separation (§3.34). This makes the logi cal development self-contained: the footnotes involving the References (pp. 214-216) are for comparison with earlier treatments, and to give credit where it is due, not to fill gaps in the argument. H.S.M.C. November 1992 v Preface to the Second Edition Why should one study the real plane? To this question, put by those who advocate the complex plane, or geometry over a general field, I would reply that the real plane is an easy first step. Most of the prop erties are closely analogous, and the real field has the advantage of intuitive accessibility. Moreover, real geometry is exactly what is needed for the projective approach to non· Euclidean geometry. Instead of introducing the affine and Euclidean metrics as in Chapters 8 and 9, we could just as well take the locus of 'points at infinity' to be a conic, or replace the absolute involution by an absolute polarity.

Author : Michele Audin
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642561276

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Geometry by Michele Audin Pdf

Geometry, this very ancient field of study of mathematics, frequently remains too little familiar to students. Michle Audin, professor at the University of Strasbourg, has written a book allowing them to remedy this situation and, starting from linear algebra, extend their knowledge of affine, Euclidean and projective geometry, conic sections and quadrics, curves and surfaces. It includes many nice theorems like the nine-point circle, Feuerbach's theorem, and so on. Everything is presented clearly and rigourously. Each property is proved, examples and exercises illustrate the course content perfectly. Precise hints for most of the exercises are provided at the end of the book. This very comprehensive text is addressed to students at upper undergraduate and Master's level to discover geometry and deepen their knowledge and understanding.

Author : Frank Sottile
Publisher : American Mathematical Soc.
Page : 214 pages
File Size : 48,9 Mb
Release : 2011-08-31
Category : Mathematics
ISBN : 9780821853313

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Real Solutions to Equations from Geometry by Frank Sottile Pdf

Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a difficult problem with many applications outside of mathematics. While it is hopeless to expect much in general, we know a surprising amount about these questions for systems which possess additional structure often coming from geometry. This book focuses on equations from toric varieties and Grassmannians. Not only is much known about these, but such equations are common in applications. There are three main themes: upper bounds on the number of real solutions, lower bounds on the number of real solutions, and geometric problems that can have all solutions be real. The book begins with an overview, giving background on real solutions to univariate polynomials and the geometry of sparse polynomial systems. The first half of the book concludes with fewnomial upper bounds and with lower bounds to sparse polynomial systems. The second half of the book begins by sampling some geometric problems for which all solutions can be real, before devoting the last five chapters to the Shapiro Conjecture, in which the relevant polynomial systems have only real solutions.

Author : Robin J. Y. McLeod,M. Louisa Baart
Publisher : Cambridge University Press
Page : 436 pages
File Size : 49,9 Mb
Release : 1998-07-13
Category : Computers
ISBN : 0521321530

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Geometry and Interpolation of Curves and Surfaces by Robin J. Y. McLeod,M. Louisa Baart Pdf

This text takes a practical, step-by-step approach to algebraic curves and surface interpolation motivated by the understanding of the many practical applications in engineering analysis, approximation, and curve-plotting problems. Because of its usefulness for computing, the algebraic approach is the main theme, but a brief discussion of the synthetic approach is also presented as a way of gaining additional insight before proceeding with the algebraic manipulation. Professionals, students, and researchers in applied mathematics, solid modeling, graphics, robotics, and engineering design and analysis will find this a useful reference.