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On a Property of Real Plane Curves of Even Degree

Part of: Curves

Published online by Cambridge University Press:  09 January 2019

Zinovy B. Reichstein
Zinovy B. Reichstein*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver BC V6T1Z2 Email: reichst@math.ubc.ca
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Abstract

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F. Cukierman asked whether or not for every smooth real plane curve $X\subset \mathbb{P}^{2}$ of even degree $d\geqslant 2$ there exists a real line $L\subset \mathbb{P}^{2}$ such $X\cap L$ has no real points. We show that the answer is yes if $d=2$ or 4 and no if $n\geqslant 6$.

Keywords

real algebraic geometryplane curvemaximizer functionbitangent

MSC classification

Primary: 14P05: Real algebraic sets
Secondary: 14H50: Plane and space curves
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 1 , March 2019 , pp. 179 - 182
Copyright
© Canadian Mathematical Society 2018 

Footnotes

The author was partially supported by NSERC Discovery Grant 253424-2017.

References

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