On the topology of surface singularities zⁿ=f(x,y), for f irreducible

2007/08/23 by Elizabeth Sell, Sell, Elizabeth A.
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.0708.3174

Abstract

The splice quotients are an interesting class of normal surface singularities with rational homology sphere links, defined by W. Neumann and J. Wahl. If Gamma is a tree of rational curves that satisfies certain combinatorial conditions, then there exist splice quotients with resolution graph Gamma. Suppose the equation zⁿ=f(x,y) defines a surface X_f,n with an isolated singularity at the origin in C³. For f irreducible, we completely characterize, in terms of n and a variant of the Puiseux pairs of f, those X_f,n for which the resolution graph satisfies the combinatorial conditions that are necessary for splice quotients. This result is topological; whether or not X_f,n is analytically isomorphic to a splice quotient is treated separately.

Related

• Topology, geometry, and equations of normal surface singularities
• Splice diagrams and splice-quotient surface singularities
• The geometric genus of splice-quotient singularities
• The multiplicity of abelian covers of splice quotient singularities
• The cohomology of line bundles of splice-quotient singularities