Smoothings of cyclic quotient singularities from a topological point of view

Abstract

For a smoothing Y of a 2-dimensional cyclic quotient singularity X, we construct a simple handle decomposition of Y by using a particular birational map from Y to the projective plane. The manifold Y is built up from the product of an annulus with a disk by attaching 2-handles in a manner which can be described by means of a plumbing graph. In particular, Y is homotopy equivalent to a 2-dimensional CW-complex with 1-skeleton a single circle.