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Author: Séverine Fiedler - Le Touzé
Publisher: CRC Press
ISBN: 0429838247
Category : Mathematics
Languages : en
Pages : 238
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Book Description
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
ISBN: 0429838247
Category : Mathematics
Languages : en
Pages : 238
Get Book Here
Book Description
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
ISBN: 0429838255
Category : Mathematics
Languages : en
Pages : 226
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Book Description
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: Christopher G. Gibson
Publisher: Cambridge University Press
ISBN: 9780521641401
Category : Mathematics
Languages : en
Pages : 278
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Book Description
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: Harold Hilton
Publisher:
ISBN:
Category : Curves, Algebraic
Languages : en
Pages : 422
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Book Description
Author: Julian Lowell Coolidge
Publisher: Courier Corporation
ISBN: 9780486495767
Category : Mathematics
Languages : en
Pages : 554
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Book Description
A thorough introduction to the theory of algebraic plane curves and their relations to various fields of geometry and analysis. Almost entirely confined to the properties of the general curve, and chiefly employs algebraic procedure. Geometric methods are much employed, however, especially those involving the projective geometry of hyperspace. 1931 edition. 17 illustrations.
Author: Egbert Brieskorn
Publisher:
ISBN:
Category : Curves, Algebraic
Languages : en
Pages : 744
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Book Description
Author: Maxim E. Kazaryan
Publisher: Springer
ISBN: 3030029433
Category : Mathematics
Languages : en
Pages : 231
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Book Description
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: Robert J. Walker
Publisher:
ISBN:
Category :
Languages : en
Pages : 228
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Book Description
Author: Clifford Joseph Maloney
Publisher:
ISBN:
Category : Curves, Cubic
Languages : en
Pages : 134
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Book Description
Author: Olaf Marentius Thalberg
Publisher:
ISBN:
Category : Curves, Algebraic
Languages : en
Pages : 62
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Book Description
