A Septic with 99 real Nodes
| dc.creator | Labs, Oliver | |
| dc.date | 2004-09-20 | |
| dc.date.accessioned | 2026-07-07T05:12:19Z | |
| dc.date.available | 2026-07-07T05:12:19Z | |
| dc.description | We find a surface of degree 7 in real projective three-space P^3(R) with 99 real nodes within a family of surfaces with dihedral symmetry: First, we consider this family over some small prime fields, which allows us to test all possible parameter sets using computer algebra. In this way we find some examples of 99-nodal surfaces over some of these finite fields. Then, the examination of the geometry of these surfaces allows us to determine the parameters of a 99-nodal septic in characteristic zero. This narrows the possibilities for μ(7), the maximum number of nodes on a septic, to: 99 <= μ(7) <= 104. When reducing our surface modulo 5, we even obtain a 100-nodal septic in P^3(F_5). | |
| dc.description | 11 pages, 4 figures. For more images/movies, see http://www.AlgebraicSurface.net | |
| dc.identifier | https://arxiv.org/abs/math/0409348 | |
| dc.identifier | http://arxiv.org/abs/math/0409348 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72536 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J17; 14Q10 | |
| dc.title | A Septic with 99 real Nodes | |
| dc.type | text |