On the number of connected components of the parabolic curve

Details On the number of connected components of the parabolic curve On the number of connected components of the parabolic curve

2009-04-29

arxiv.org/abs/0904.4652v1

Mathematics

Algebraic Geometry

4 pages

Scientific paper

We construct a polynomial of degree d in two variables whose
Hessian curve has (d-2)^2 connected components using Viro patchworking. In
particular, this implies the existence of a smooth real algebraic surface of
degree d in RP^3 whose parabolic curve is smooth and has d(d-2)^2 connected
components.

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