Computing resolutions of quotient singularities

2016/02/29 by Donten-Bury, Maria, Keicher, Simon
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1603.00071

Abstract

Let 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/G, which is based just on the geometry of the singularity ℂⁿ/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/G for all G⊆ GL(3) with the aforementioned property and of order |G|≤ 12. We also provide examples in dimension 4.

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