A new linear quotient of C4 admitting a symplectic resolution

We show that the quotient C 4 / G admits a symplectic resolution for . Here Q 8 is the quaternionic group of order eight and D 8 is the dihedral group of order eight, and G is the quotient of their direct product which identifies the nontrivial central elements −Id of each. It is equipped with the t...

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Bibliographic Details
Published inMathematische Zeitschrift Vol. 273; no. 3-4; pp. 753 - 769
Main Authors Bellamy, Gwyn, Schedler, Travis
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 2013
Subjects
Mathematics
Mathematics and Statistics
Symplectic resolution
Poisson variety
17B63
Symplectic smoothing
McKay correspondence
16S80
Poisson algebra
Symplectic leaves
Symplectic reflection algebra
Quotient singularity
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Summary:We show that the quotient C 4 / G admits a symplectic resolution for . Here Q 8 is the quaternionic group of order eight and D 8 is the dihedral group of order eight, and G is the quotient of their direct product which identifies the nontrivial central elements −Id of each. It is equipped with the tensor product representation . This group is also naturally a subgroup of the wreath product group . We compute the singular locus of the family of commutative spherical symplectic reflection algebras deforming C 4 / G . We also discuss preliminary investigations on the more general question of classifying linear quotients V / G admitting symplectic resolutions.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-012-1028-6