• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.951-973
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• 1997

We classify up to conjugation all finite abelian subgroups of $GL(2,C)$ of order $\leq 18$ and compute the generators and relations of their rings of invariants. In other words, we classify all 2-dimensional quotient singularities by an abelian group of order $\leq 18$ and compute the generators and relations of their affine coordinate rings.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.419-437
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• 2021

We prove that every minimal symplectic filling of the link of a quotient surface singularity can be obtained from its minimal resolution by applying a sequence of rational blow-downs and symplectic antiflips. We present an explicit algorithm inspired by the minimal model program for complex 3-dimensional algebraic varieties.