Smooth three-dimensional canonical thresholds

If X is an algebraic variety with at most canonical singularities and S is a ?-Cartier hypersurface in X, then the canonical threshold of the pair (X, S) is defined as the least upper bound of the reals c for which the pair (X, cS) is canonical. We show that the set of all possible canonical thresholds of the pairs (X, S), where X is smooth and three-dimensional, satisfies the ascending chain condition. We also derive a formula for the canonical threshold of the pair (?³, S), where S is a Brieskorn singularity.