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 ${\mathbb{C}}^{\ast }$ in ${\mathbb{C}}^2$ with no self-intersections can have at most three cuspidal singularities.

arXiv comment15 pages, to appear in Ann. Inst. Fourier