Multiple Structures on Smooth on Singular Varieties

Abstract

Let k an algebraically closed field, char k = 0. Let C be an irreducible nonsingular curve such that rC = S ∩ F, $r\in \mathbb {N}$, where S and F are two surfaces in $\mathbb {P}^3$ and all the singularities of F are of the form z ^p = x ^ps − y ^ps, p prime, $s\in \mathbb {N}$. We prove that C can never pass through such kind of singularities of a surface, unless r = pa, $a\in \mathbb {N}$. These singularities are Kodaira singularities.

Dedicated to Professor Antonio Campillo