Real plane algebraic curves with asymptotically maximal number of even ovals
نویسندگان
چکیده
منابع مشابه
Real Plane Algebraic Curves with Asymptotically Maximal Number of Even Ovals
It is known for a long time that a nonsingular real algebraic curve of degree 2k in the projective plane cannot have more than 7k 2 2 − 9k 4 + 3 2 even ovals. We show here that this upper bound is asymptotically sharp, that is to say we construct a family of curves of degree 2k such that p k →k→∞ 7 4 , where p is the number of even ovals of the curves. We also show that the same kind of result ...
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F. Cukierman asked whether or not for every smooth real plane curve X ⊂ P of even degree d > 2 there exists a real line L ⊂ P such X ∩ L has no real points. We show that the answer is “yes” if d = 2 or 4 and “no” if n > 6.
متن کاملA tropical construction of a family of reducible curves.dvi
We give a constructive proof using tropical modifications of the existence of a family of real algebraic plane curves with asymptotically maximal numbers of even ovals.
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2006
ISSN: 0012-7094
DOI: 10.1215/s0012-7094-06-13136-8