Equations of low-degree Projective Surfaces with three-divisible Sets of Cusps

Details Equations of low-degree Projective Surfaces with three-divisible Sets of Cusps Equations of low-degree Projective Surfaces with three-divisible Sets of Cusps

2001-12-05

arxiv.org/abs/math/0112046v2

Mathematics

Algebraic Geometry

13 pages; a discussion of the family of quintics with 12 three-divisible cusps added

Scientific paper

Let Y be a surface with only finitely many singularities all of which are
cusps. A set of cusps on Y is called three-divisible, if there is a cyclic
global triple cover of Y branched precisely over these cusps. The aim of this
note is to determine the equations of surfaces $Y \subset P_3$ of degrees $\leq
6$ carrying a minimal, non-empty, three-divisible set.

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