Totally real pencils of cubics with respect to sextics

2013/03/18 by Séverine Fiedler-Le Touzé, Touzé, Séverine Fiedler-Le · 1 citation
Computer Science · Mathematics · #Commutative Algebra and Its Applications #Mathematics and Applications #Polynomial and algebraic computation #math.AG #msc:14P25

paper · pdf · doi:10.48550/arxiv.1303.4341

9 pages, 3 figures

arxiv created 2013/03/18 · arxiv updated 2013/03/19

Abstract

A real algebraic plane curve A is said to be dividing if its real part ℝA disconnects its complex part ℂA. A pencil of curves is totally real with respect to A if it has only real intersections with ℂA. If there exists such a pencil, then A is dividing, this is the case for the M-curves. Can conversely any dividing curve be endowed with a totally real pencil? We study here the case of M-2-sextics having 2 or 6 empty exterior ovals. Such sextics are always dividing. We prove that they may actually be endowed with a totally real pencil of cubics.

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• The separating semigroup of a real curve

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