A GAGA type theorem on germs of analytic curves through germs of quotient surface singularities
type: Item
instance of: scholarly article
title: A GAGA type theorem on germs of analytic curves through germs of quotient surface singularities
zbMATH Open document ID: 0799.32029
DOI: 10.1007/BF01201782
author: Raimund Blache
published in: Archiv der Mathematik
publication date: 1994-11-24T00:00:00Z
review text: The author proves that the germ of a reduced complex analytic curve \((C,x)\) through a quotient singularity \((X,x)\) of dimension two is biholomorphic to the germ \((Y,D,y)\) of a projective curve on a projective surface. Along the way he gives an explicit description of the divisor class group of a quotient singularity. A detailed, self-contained proof is given; the key point is that equivariant functions on \((\mathbb{C}^ 2,0)\) with isolated singularity are finitely determined. The proper context, especially for generalisations, is the theory of ``geometrically defined subgroups of \({\mathcal A}\) and \({\mathcal K}\)'' [cf. \textit{J. Damon}, Proc. Symp. Pure Math. 40, Part 1, 233- 254 (1983; Zbl 0519.58014)].
Mathematics Subject Classification ID: 32S25
Mathematics Subject Classification ID: 14B05
zbMATH DE Number: 563366
zbMATH Keywords: divisor class group
zbMATH Keywords: quotient singularity
reviewed by: Jan Stevens
MaRDI profile type: Publication
cites work: Q3953883
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description: scientific article; zbMATH DE number 563366