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On a property of real plane curves of even degree

  • Zinovy B. Reichstein,
    Department of Mathematics, University of British Columbia, Vancouver BC V6T1Z2, Canada
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Abstract

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 geometry, plane curve, maximizer function, bitangent real algebraic geometry, plane curve, maximizer function, bitangent
MSC Classifications: 14P05, 14H50 show english descriptions Real algebraic sets [See also 12Dxx, 13P30]
Plane and space curves
14P05 - Real algebraic sets [See also 12Dxx, 13P30]
14H50 - Plane and space curves
 

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