Part 1 of this book answers questions for using rational cubics and pencils of cubics. Part 2 deals with configurations of eight points in convex position. Part 3 contains applications and results around Hilbert's sixteenth problem.
Part 1 of this book answers questions for using rational cubics and pencils of cubics. Part 2 deals with configurations of eight points in convex position. Part 3 contains applications and results around Hilbert's sixteenth problem.
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.
Inhaltsangabe
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
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
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