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

Abstract

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 $\le 6$ carrying a minimal, non-empty, three-divisible set.

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

References in corpus (1)

• K3 Surfaces with Nine Cusps

Cited by in corpus (4)

• Defect and Hodge numbers of hypersurfaces
• Cusps and Codes
• Cuspidal quintics and surfaces with $p_g=0,$ $K^2=3$ and 5-torsion
• Wolf Barth (1942--2016)