  We prove the Goldman-Parker Conjecture: A complex hyperbolic ideal triangle
group is directly embedded in PU(2,1) if and only if the product of its three
standard generators is not elliptic. We also prove that such a group is
indiscrete if the product of its three standard generators is elliptic. A novel
feature of this paper is that it uses a rigorous computer assisted proof to
deal with difficult geometric estimates.
