Pencils of Cubics and Algebraic Curves in the Real Projective Plane
CRC Press (Verlag)
978-1-138-59051-9 (ISBN)
Part 2 deals with configurations of eight points in convex position.
Part 3 contains applications and results around Hilbert’s sixteenth problem.
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.
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.
I Rational pencils of cubics and configurations of six or seven points in RP 2
1 Points, lines and conics in the plane
2 Configurations of six points
3 Configurations of seven points
II Pencils of cubics with eight base points lying in convex position in RP 2
4 Pencils of cubics
5 Lists of conics
6 Link between lists and pencils
7 Pencils with reducible cubics
8 Classification of the pencils of cubics
9 Tabulars
10 Application to an interpolation problem
III Algebraic curves
11 Hilbert’s 16th problem
12 M -curves of degree 9
13 M -curves of degree 9 with deep nests
14 M -curves of degree 9 with four or three nests
15 M -curves of degree 9 or 11 with one non-empty oval
16 Curves of degree 11 with many nests
17 Totally real pencils of curves
| Erscheinungsdatum | 04.10.2018 |
|---|---|
| Zusatzinfo | 62 Tables, black and white; 107 Illustrations, black and white |
| Verlagsort | London |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 453 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-138-59051-7 / 1138590517 |
| ISBN-13 | 978-1-138-59051-9 / 9781138590519 |
| Zustand | Neuware |
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