A Sextic with 35 Cusps

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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.
6 pages, 1 figure, for additional images/movies, see http://www.AlgebraicSurface.net

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Algebraic Geometry, Commutative Algebra, 14J17; 14Q10

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http://salesiana.dossiersoluciones.com/handle/123456789/74311

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0502520
 http://arxiv.org/abs/math/0502520

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arXiv