  We prove the "End Curve Theorem," which states that a normal surface
singularity $(X,o)$ with rational homology sphere link $\Sigma$ 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 $\Sigma$ 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 its universal abelian cover as a complete
intersection in $\C^t$, where $t$ is the number of leaves in the resolution
graph for $(X,o)$, together with an explicit description of the covering
transformation group.
  Among the immediate consequences of the End Curve Theorem are the previously
known results: $(X,o)$ is a splice quotient if it is weighted homogeneous
(Neumann 1981), or rational or minimally elliptic (Okuma 2005).
