The canonical filtration of higher dimensional purely elliptic singularity of a special type

Tomari, Masataka

doi:10.1007/bf01245087

Cited by 8 publications

(14 citation statements)

References 29 publications

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“…The rationality of UX Y D is studied already in our previous works; Lemma (3.1) and Example (3.5) of [20], O3 and O4 of [22], O5 of [17], and Proposition (1.5) of [16]. The following result uni®es various statements in [20,21].…”

Section: Hdivu Q Hdivrymentioning

confidence: 61%

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Cyclic covers of normal graded rings

Tomari¹,

Watanabe²

2001

Kodai Math. J.

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We give a description of a graded cyclic cover of a normal graded ring in terms of the Pinkham-Demazure description of normal graded rings R RX Y D. With the geometric description of ClR, it is shown that our cyclic cover S possesses the Pinkham-Demazure description S q RY YD [Theorem 1.3], by which we obtain a description of an index one cover [Corollary 1.7] of R. In O2, as an application of this description, we give criteria for the normal graded singularities to be Kawamata log terminal or to be log canonical. Further, in O3 we study the relations between cyclic covers of the Kummer type and cyclic covers obtained by using Veronese subrings. Our results extend S. Mori's structure theorem regarding graded factorial domains.

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Section: Hdivu Q Hdivrymentioning

confidence: 61%

“…Proof (cf. [7,16]). If a H`0 , then, as we have already seen, R is a klt singularity of index r with respect to K R DE by Theorem 2.6.…”

Section: ) This Completesmentioning

confidence: 99%

Cyclic covers of normal graded rings

Tomari¹,

Watanabe²

2001

Kodai Math. J.

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“…Moreover, we have the following result, proved by Tomari [23] (see also [26 There is a list of Sing(K ′ ) for 95 weight-vectors in [26]. The following are well-defined:…”

mentioning

confidence: 74%

The topological types of hypersurface simple K 3 singularities

Katanaga

2013

Topology and its Applications

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We give a result that relates the diffeomorphism type of the link of a nondegenerate semi-quasi-homogeneous hypersurface simple K3 singularity with the singularities of the normal K3 surface that appears as the exceptional divisor of the resolution of the singularity. As a result, we show that the links are diffeomorphic to the connected sum of copies of S 2 × S 3 . Moreover, we also show that the topological types of hypersurface simple K3 singularities defined by non-degenerate semi-quasihomogeneous polynomials are all different.

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“…In fact, F is determined by the valuation corresponding to the exceptional divisor on the canonical model. We called this "the canonical filtration " [18]. Theorem (4.3.2)(cf.…”

Section: Special Cases: the Purely Elliptic Singularitiesmentioning

confidence: 99%

“…(4.10.2) X 6,18 ⊂ P (1,3,5,6,9) as the second Veronesian of X 36 ⊂ P (1,5,12,18). (4.10.3) X 8,24 ⊂ P (3,4,5,8,12) as the second Veronesian of X 48 ⊂ P (3,5,16,24).…”

Section: Remark (47)mentioning

confidence: 99%

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

Ishii¹,

Tomari²

2001

Math Z

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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(≥ 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.

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The canonical filtration of higher dimensional purely elliptic singularity of a special type

Cited by 8 publications

References 29 publications

Cyclic covers of normal graded rings

Cyclic covers of normal graded rings

The topological types of hypersurface simple K 3 singularities

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

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