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15 February 2006 Real plane algebraic curves with asymptotically maximal number of even ovals
Erwan Brugallé
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Duke Math. J. 131(3): 575-587 (15 February 2006). DOI: 10.1215/S0012-7094-06-13136-8

Abstract

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 7k2/4-9k/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/k2k7/4, 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

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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

Information

Published: 15 February 2006
First available in Project Euclid: 6 February 2006

zbMATH: 1109.14040
MathSciNet: MR2219251
Digital Object Identifier: 10.1215/S0012-7094-06-13136-8

Subjects:
Primary: 12D10 , 14H50 , 14P25
Secondary: 05A16

Rights: Copyright © 2006 Duke University Press

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Vol.131 • No. 3 • 15 February 2006
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