On the topology of surface singularities {z^n=f(x,y)}, for f irreducible

Details On the topology of surface singularities {z^n=f(x,y)}, for f irreducible On the topology of surface singularities {z^n=f(x,y)}, for f irreducible

2007-08-23

arxiv.org/abs/0708.3174v2

Mathematics

Algebraic Geometry

25 pages, 18 figures; v2: typos and errors corrected, organizational changes made, references updated; to appear in Michigan M

Scientific paper

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 z^n=f(x,y) defines a surface X_{f,n} with an isolated singularity at the origin in C^3. 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.

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