## Partial resolutions of quotient singularities.(English)Zbl 0791.14005

For quotient singularities, the irreducible components of the (reduced) base space of the versal deformation are in one to one correspondence with certain partial resolutions, called $$P$$-resolutions. In this note, the author determines all $$P$$-resolutions for quotient singularities, in fact, with a simple lemma, he reduces the general problem to the special case of cyclic quotient singularities which he studied in a previous paper [cf. Singularity theory and applications. Part I: Geometric aspects of singularities. Proc. Symp., Warwick 1988/89, Lect. Notes Math. 1462, 302-319 (1991; Zbl 0747.14002)].

### MSC:

 14E15 Global theory and resolution of singularities (algebro-geometric aspects) 14M17 Homogeneous spaces and generalizations 32S45 Modifications; resolution of singularities (complex-analytic aspects)

### Keywords:

$$P$$-resolutions; quotient singularities

Zbl 0747.14002
Full Text:

### References:

 [1] J. Kollár and N. I. Shepherd-Barron,Threefolds and deformations of surface singularities. Invent. math.91 (1988), 299-338 · Zbl 0642.14008 [2] Oswald Riemenschneider,Zweidimensionale Quotientensingularitäten: Gleichungen und Syzygien. Archiv der Math.37 (1981), 406-417 · Zbl 0456.14006 [3] Stevens, Jan, On the versal deformation of cyclic quotient singularities, No. 1462, 312-319 (1991), Berlin etc. · Zbl 0747.14002
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