On the Craw–Ishii conjecture

Seung Jo Jung

doi:10.1016/j.jpaa.2017.07.013

On the Craw–Ishii conjecture

Seung Jo Jung

Department of Mathematics Education

Korea Institute for Advanced Study

Research output: Contribution to journal › Journal article › peer-review

3 Scopus citations

Abstract

In [2], Craw and Ishii proved that for a finite abelian group G⊂SL₃(C) every (projective) relative minimal model of C³/G is isomorphic to the fine moduli space M_θ of θ-stable G-constellations for some GIT parameter θ. In this article, we conjecture that the same is true for a finite group G⊂GL₃(C) if a relative minimal model Y of X=C³/G is smooth. We prove this for some abelian groups.

Original language	English
Pages (from-to)	1579-1605
Number of pages	27
Journal	Journal of Pure and Applied Algebra
Volume	222
Issue number	7
DOIs	https://doi.org/10.1016/j.jpaa.2017.07.013
State	Published - 2018.07

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title = "On the Craw–Ishii conjecture",

abstract = "In [2], Craw and Ishii proved that for a finite abelian group G⊂SL3(C) every (projective) relative minimal model of C3/G is isomorphic to the fine moduli space Mθ of θ-stable G-constellations for some GIT parameter θ. In this article, we conjecture that the same is true for a finite group G⊂GL3(C) if a relative minimal model Y of X=C3/G is smooth. We prove this for some abelian groups.",

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AB - In [2], Craw and Ishii proved that for a finite abelian group G⊂SL3(C) every (projective) relative minimal model of C3/G is isomorphic to the fine moduli space Mθ of θ-stable G-constellations for some GIT parameter θ. In this article, we conjecture that the same is true for a finite group G⊂GL3(C) if a relative minimal model Y of X=C3/G is smooth. We prove this for some abelian groups.

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DO - 10.1016/j.jpaa.2017.07.013

M3 - Journal article

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VL - 222

SP - 1579

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JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

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ER -

On the Craw–Ishii conjecture

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