Computing resolutions of quotient singularities

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• 作者：Maria Donten-Bury^a ; ^b ; ^{m.donten@mimuw.edu.pl} ; Simon Keicher^c ; ^{keicher@mail.mathematik.uni-tuebingen.de}
• 关键词：14E15 ; 14Q10 ; 14Q15 ; 14C20 ; 14L24
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：472
• 期：Complete
• 页码：546-572
• 全文大小：537 K
• 卷排序：472

文摘

Let G⊆GL(n)G⊆GL(n) be a finite group without pseudo-reflections. We present an algorithm to compute and verify a candidate for the Cox ring of a resolution X→Cn/GX→Cn/G, which is based just on the geometry of the singularity Cn/GCn/G, without further knowledge of its resolutions. We explain the use of our implementation of the algorithms in Singular. As an application, we determine the Cox rings of resolutions X→C3/GX→C3/G for all G⊆GL(3)G⊆GL(3) with the aforementioned property and of order |G|≤12|G|≤12. We also provide examples in dimension 4.