Real plane algebraic curves with asymptotically maximal number of even ovals
| dc.creator | brugalle, Erwan | |
| dc.date | 2004-11-04 | |
| dc.date.accessioned | 2026-07-07T05:13:58Z | |
| dc.date.available | 2026-07-07T05:13:58Z | |
| dc.description | It 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.description | 12 pages, 10 figures | |
| dc.identifier | https://arxiv.org/abs/math/0411097 | |
| dc.identifier | http://arxiv.org/abs/math/0411097 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73109 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Real plane algebraic curves with asymptotically maximal number of even ovals | |
| dc.type | text |