Abstract
It has been known for a long time that a nonsingular real algebraic curve of degree in the projective plane cannot have more than even ovals. We show here that this upper bound is asymptotically sharp; that is to say, we construct a family of curves of degree such that , where 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
Citation
Erwan Brugallé. "Real plane algebraic curves with asymptotically maximal number of even ovals." Duke Math. J. 131 (3) 575 - 587, 15 February 2006. https://doi.org/10.1215/S0012-7094-06-13136-8
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