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We prove the “End Curve Theorem,” which states that a normal surface singularity $(X, o)$ with rational homology sphere link $Σ$ is a splice quotient singularity if and only if it has an end curve function for each leaf of a good resolution tree. An “end curve function” is an analytic function $(X, o) \to (ℂ, 0)$ whose zero set intersects $Σ$ in the knot given by a meridian curve of the exceptional curve corresponding to the given leaf. A “splice quotient singularity” $(X, o)$ is described by giving an explicit set of equations describing...

Local Contributions to Global Deformations of Surfaces.

Jonathan M. Wahl; D.M. Jr. Burns — 1974

Inventiones mathematicae

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Complete intersection singularities of splice type as universal Abelian covers.

Complex surface singularities with integral homology sphere links.

Deformations of Quasi-Homogeneous Surface Singularities.

Second Chern class and Riemann-Roch for vector bundles on resolutions of surface singularities.

Gaussian Maps and Tensor products of irreducible representations.

Elliptic Deformations of Minimally Elliptic Singularities.

Derivations of Negative Weight and Non-Smoothability of Certain Singularities.

Simultaneous resolution of rational singularities

Vanishing Theorems for Resolutions of Surfaces Singularities.

A characterization of quasi-homogeneous Gorenstein surface singularities

Equations defining rational singularities

Casson invariant of links of singularities.

The end curve theorem for normal complex surface singularities

Local Contributions to Global Deformations of Surfaces.