Number of singular points of an annulus in $\mathbb{C}^2$

Abstract

Using Bogomolov-Miyaoka-Yau inequality and a Milnor number bound we prove that any algebraic annulus $\mathbb{C}^*$ in $\mathbb{C}^2$ with no self-intersections can have at most three cuspidal singularities.Comment: 15 pages, to appear in Ann. Inst. Fourie