On a Property of Real Plane Curves of Even Degree
Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 179-182
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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 $n\geqslant 6$.
Mots-clés :
real algebraic geometry, plane curve, maximizer function, bitangent
Reichstein, Zinovy B. On a Property of Real Plane Curves of Even Degree. Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 179-182. doi: 10.4153/CMB-2017-065-7
@article{10_4153_CMB_2017_065_7,
author = {Reichstein, Zinovy B.},
title = {On a {Property} of {Real} {Plane} {Curves} of {Even} {Degree}},
journal = {Canadian mathematical bulletin},
pages = {179--182},
year = {2019},
volume = {62},
number = {1},
doi = {10.4153/CMB-2017-065-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-065-7/}
}
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