Smooth three-dimensional canonical thresholds

If X is an algebraic variety with at most canonical singularities and S is a ℚ-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 (ℂ 3 , S ), where S is a Brieskorn singularity.