A note on P-resolutions of cyclic quotient singularities

1997/03/19 by Ludwig Balke, Balke, Ludwig
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9703024

8 pages, 4 Postscript figures

arxiv created 1997/03/19 · openalex publication_date 1997/03/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

P-resolutions of a cyclic quotient singularity are known to be in one-to-one correspondence with the components of the base space of its semi-universal deformation. Stevens and Christophersen have shown that P-resolutions are parametrized by so-called chains representing zero or, equivalently, certain subdivisions of polygons. I give here a purely combinatorial proof of the correspondence between subdivisions of polygons and P-resolutions.

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