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Pencils of Cubics and Algebraic Curves in the Real Projective Plane book cover

1st Edition

Pencils of Cubics and Algebraic Curves in the Real Projective Plane

By Séverine Fiedler - Le Touzé Copyright 2019
256 Pages 107 B/W Illustrations
by Chapman & Hall

256 Pages 107 B/W Illustrations
by Chapman & Hall

256 Pages 107 B/W Illustrations
by Chapman & Hall
Also available as eBook on:
Pencils of Cubics and Algebraic Curves in the Real Projective Plane thoroughly examines the combinatorial configurations of n generic points in R P ². 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... Read more

Rational pencils of cubics and configurations of six or seven points in RP²

Points, lines and conics in the plane

Configurations of six points

Configurations of seven points

Pencils of cubics with eight base points lying in convex position in RP²

Pencils of cubics

List of conics

Link between lists and pencils

Pencils with reducible cubics

Classification of the pencils of cubics

Tabulars

Application to an interpolation problem

Algebraic curves

Hilbert’s 16th problem

M-curves of degree 9

M-curves of degree 9 with deep nests

M-curves of degree 9 with four or three nests

M-curves of degree 9 or 11 with non-empty oval

Curves of degree 11 with many nests

Totally real pencils of curves

Biography

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.

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