Masataka Tomari

NormalZ r-graded rings and normal cyclic covers

We give a description of a cyclic cover of a normal domain in terms of a rational coefficient divisor and an element of the quotient field of the base domain. Then we study the integrity, the normality, the divisor class group and the Gorenstein property of the cyclic cover by our description ((1.9), (1.12), (2.6), (3.2), (3.3)). Also we characterize the regularity, of it in terms of the divisor and singularities of base domain ((3.11)). As an application, we can give the necessary and sufficient condition for a normal graded ring over a field to have an isolated singularity in terms of Demazures construction of normal graded rings ((4.1)).

On L 2 -Plurigenera of not-Log-Canonical Gorenstein Isolated Singularities

We will give an application of S. Izumis theorems of order functions of analytic spaces to classification problems of isolated singularities by means of plurigenus 3m .

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

Abstract. We study the Newton boundaries of hypersurface singularities from the viewpoint of the theory of filtered blowing-ups. We can construct counter examples to Reids conjecture in the

On singularities arising from the contraction op the minimal section of a ruled surface

d (\geq 3)

Filtered Rings, Filtered Blowing-Ups and Normal Two-Dimensional Singularities with "Star-Shaped" Resolution

-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

The Inequality 8pg < μ for Hypersurface Two‐dimensional Isolated Double Points

We will discuss the Gorenstein property of the singularity which is blown down from the minimal section of a ruled surface in terms of the extension class. In the case that the base field has positive characteristic, we find a new example (3.4) of Gorenstein singularity in connection with Theorem B.