On two-dimensional quasihomogeneous isolated singularities, II

Herzog, Jürgen

doi:10.1007/bf01194847

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Introduction and Historical Remarks1

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1993

2008

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Cited by 3 publications

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“…The reason for this terminology will be explained below in Remark 4.17. [51] that if the ring A is Gorenstein, D ∼ = (Ω 1 A ) * * and the canonical morphism…”

Section: Introduction and Historical Remarksmentioning

confidence: 99%

Maximal Cohen–Macaulay modules over surface singularities

Burban¹,

Drozd²

2008

Trends in Representation Theory of Algebras and Related Topics

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“…The reason for this terminology will be explained below in Remark 4.17. [51] that if the ring A is Gorenstein, D ∼ = (Ω 1 A ) * * and the canonical morphism…”

Section: Introduction and Historical Remarksmentioning

confidence: 99%

Maximal Cohen–Macaulay modules over surface singularities

Burban¹,

Drozd²

2008

Trends in Representation Theory of Algebras and Related Topics

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Gluing Cohen-Macaulay modules with applications to quasihomogeneous complete intersections with isolated singularities

Herzog¹,

Martsinkovsky²

1993

Commentarii Mathematici Helvetici

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Auslander Modules and Quasi-Homogeneity of Local Rings

Yoshino¹,

Kato²

1994

Publ. Res. Inst. Math. Sci.

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§0. IntroductionLet (R,m,k) be a normal local domain of dimension two and assume that k is an algebraically closed field of characteristic zero. Let us denote K R the canonical module of R. Then from the definition of K R , there are isomorphisms:which involves the unique existence of the nonsplit exact sequence:The J?-module A which appears in the sequence is also uniquely determined except for isomorphisms, and is called the Auslander module of R. (For more details, see [13; Chapter 11].) In this paper, it is of our main interest how the Auslander module is related to the quasi-homogeneity of a local ring. Here recall that R is said to be quasi-homogeneous if it is the completion of a positively graded ring, or equivalently if it has an Euler derivation, i.e. â -derivation A with the property that for some system of generators X l9 X 2 , • • •, X n of m and positive integers d l ,d 2 , --,d n . Now to fix our attention onto a ring of hypersurface singularity, we put R = P/fP where P = k [[X, F,Z]] is the formal power series ring and

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On two-dimensional quasihomogeneous isolated singularities, II

Cited by 3 publications

References 5 publications

Maximal Cohen–Macaulay modules over surface singularities

Maximal Cohen–Macaulay modules over surface singularities

Gluing Cohen-Macaulay modules with applications to quasihomogeneous complete intersections with isolated singularities

Auslander Modules and Quasi-Homogeneity of Local Rings

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