Real plane algebraic curves with asymptotically maximal number of even ovals
Brugallé, Erwan
Duke Math. J., Tome 131 (2006) no. 1, p. 575-587 / Harvested from Project Euclid
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It has been known for a long time that a nonsingular real algebraic curve of degree $2k$ in the projective plane cannot have more than ${7k^2}/{4}-{9k}/{4}+{3}/{2}$ 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 ${p}/{k^2}\to_{k\to\infty} {7}/{4}$ , where $p$ is the number of even ovals of the curves. We also show that the same kind of result is valid when dealing with odd ovals
Publié le : 2006-02-15
Classification:  14P25,  12D10,  14H50,  05A16 
@article{1139232350,
     author = {Brugall\'e, Erwan},
     title = {Real plane algebraic curves with asymptotically maximal number of even ovals},
     journal = {Duke Math. J.},
     volume = {131},
     number = {1},
     year = {2006},
     pages = { 575-587},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1139232350}
}

Brugallé, Erwan. Real plane algebraic curves with asymptotically maximal number of even ovals. Duke Math. J., Tome 131 (2006) no. 1, pp.  575-587. http://gdmltest.u-ga.fr/item/1139232350/