Real plane algebraic curves with asymptotically maximal number of even ovals

dc.creatorbrugalle, Erwan
dc.date2004-11-04
dc.date.accessioned2026-07-07T05:13:58Z
dc.date.available2026-07-07T05:13:58Z
dc.descriptionIt is known for a long time that a nonsingular real algebraic curve of degree 2k in the projective plane cannot have more than 7/2*k^2-9/4*k+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 tends to 7/4$ as k tends to infinity, where p is the number of even ovals of the curves. We also show that the same kind of result is valid dealing with odd ovals.
dc.description12 pages, 10 figures
dc.identifierhttps://arxiv.org/abs/math/0411097
dc.identifierhttp://arxiv.org/abs/math/0411097
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73109
dc.subjectAlgebraic Geometry
dc.titleReal plane algebraic curves with asymptotically maximal number of even ovals
dc.typetext

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