A Sextic with 35 Cusps
| dc.creator | Labs, Oliver | |
| dc.date | 2005-02-24 | |
| dc.date.accessioned | 2026-07-07T05:17:27Z | |
| dc.date.available | 2026-07-07T05:17:27Z | |
| dc.description | Recently, W. Barth and S. Rams discussed sextics with up to 30 $A_2$-singularities (also called cusps) and their connection to coding theory [math.AG/0403018]. In the present paper, we find a sextic with 35 cusps within a four-parameter family of surfaces of degree 6 in projective three-space with dihedral symmetry $D_5$. This narrows the possibilities for the maximum number $μ_{A_2}(6)$ of $A_2$-singularities on a sextic to $35 \le μ_{A_2}(6) \le 37$. To construct this surface, we use a general algorithm in characteristic zero for finding hypersurfaces with many singularities within a family. | |
| dc.description | 6 pages, 1 figure, for additional images/movies, see http://www.AlgebraicSurface.net | |
| dc.identifier | https://arxiv.org/abs/math/0502520 | |
| dc.identifier | http://arxiv.org/abs/math/0502520 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74311 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14J17; 14Q10 | |
| dc.title | A Sextic with 35 Cusps | |
| dc.type | text |