Danilov's resolution and representations of the McKay quiver

Kędzierski, Oskar

doi:10.2748/tmj/1412783203

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…C 3 =G, there is a generic stability parameter y such that Y G M y . See [Kę14], [NdCS17], [Jun16] and [Jun18] for related results.…”

Section: Introductionmentioning

confidence: 99%

$G$-constellations and the maximal resolution of a quotient surface singularity

Ishii¹

2020

Hiroshima Math. J.

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For a finite subgroup G of GLð2; CÞ, we consider the moduli space M y of G-constellations. It depends on the stability parameter y and if y is generic it is a resolution of singularities of C 2 =G. In this paper, we show that a resolution Y of C 2 =G is isomorphic to M y for some generic y if and only if Y is dominated by the maximal resolution under the assumption that G is abelian or small. 2010 Mathematics Subject Classification. 14D20; 14E16; 14J17. Key words and phrases. G-constellation, quotient singularity, maximal resolution. G-constellations onthat H 0 ðEÞ is isomorphic to the regular representation of G as a C½G-module.

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“…C 3 =G, there is a generic stability parameter y such that Y G M y . See [Kę14], [NdCS17], [Jun16] and [Jun18] for related results.…”

Section: Introductionmentioning

confidence: 99%

$G$-constellations and the maximal resolution of a quotient surface singularity

Ishii¹

2020

Hiroshima Math. J.

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“…The main result of [CI04] is that for a finite abelian subgroup G ⊂ SL(3, C) and for a projective crepant resolution Y → C 3 /G, there is a generic stability parameter θ such that Y ∼ = M θ . See [Kę14], [NdCS17], [Jun16] and [Jun17] for related results.…”

Section: Introductionmentioning

confidence: 99%

$G$-constellations and the maximal resolution of a quotient surface singularity

Ishii¹

2017

Preprint

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For a finite subgroup G of GL(2, C), we consider the moduli space M θ of G-constellations. It depends on the stability parameter θ and if θ is generic it is a resolution of singularities of C 2 /G. In this paper, we show that a resolution Y of C 2 /G is isomorphic to M θ for some generic θ if and only if Y is s dominated by the maximal resolution under the assumption that G is abelian or small. G-constellations on C n DefinitionsLet V = C n be an affine space and G ⊂ GL(V ) a finite subgroup.

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Terminal quotient singularities in dimension three via variation of GIT

Jung

2016

Journal of Algebra

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Danilov's resolution and representations of the McKay quiver

Cited by 3 publications

References 14 publications

$G$-constellations and the maximal resolution of a quotient surface singularity

$G$-constellations and the maximal resolution of a quotient surface singularity

$G$-constellations and the maximal resolution of a quotient surface singularity

Terminal quotient singularities in dimension three via variation of GIT

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