Hypersurface non-rational singularities which look canonical from their Newton boundaries

摘要

We study the Newton boundaries of hypersurface singularities from the viewpoint of the theory of filtered blowing-ups. We can construct counter examples to Reid's conjecture in the d(greater than or equal to 3)-dimensional cases which is related to the problem about the existence of good embedding for the criterion about the rationality (or the non-rationality). For 3-dimensional case, our examples contains a simple K3 singularity which does not belong to the famous list consisting of 95 types. [References: 31]