Pencils of Cubics and Algebraic Curves in the Real Projective Plane

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.

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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.