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The end curve theorem for normal complex surface singularities

Walter D. NeumannJonathan Wahl — 2010

Journal of the European Mathematical Society

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 ) ( , 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...

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