Smoothings of cyclic quotient singularities from a topological point of view

1999/11/10 by Ludwig Balke, Balke, Ludwig
Mathematics · #32S30 (Primary) 32S55 #57M50 (Secondary) #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #math.AG #math.GT #msc:32S30 #msc:32S55 #msc:57M50

paper · pdf · doi:10.48550/arxiv.math/9911070

11 pages, 13 figures

arxiv created 1999/11/10 · openalex publication_date 1999/11/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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