A new linear quotient of C 4 admitting a symplectic resolution
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209_2012_Article_1028.pdf
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Author(s)
Bellamy, Gwyn
Schedler, Travis
Date Issued
April 2012
Journal
Mathematische Zeitschrift
Publisher
Springer-Verlag
Citation
Bellamy, Gwyn, and Travis Schedler. “A New Linear Quotient of C 4 Admitting a Symplectic Resolution.” Mathematische Zeitschrift 273.3–4 (2013): 753–769.
Version
Author's final manuscript
Abstract
We show that the quotient C[superscript 4]/G admits a symplectic resolution for G = Q[subscript 8] x [subscript Z/2]D[subscript 8] < Sp[subscript 4](C). Here Q[subscript 8] is the quaternionic group of order eight and D[subscript 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 C[superscript 2] ⊠ C[superscript 2] ≅ C[superscript 4]. This group is also naturally a subgroup of the wreath product group Q[superscript 8][subscript 2] ⋊ S[subscript 2] < Sp[subscript 4](C). We compute the singular locus of the family of commutative spherical symplectic reflection algebras deforming C[superscript 4]/G. We also discuss preliminary investigations on the more general question of classifying linear quotients V/G admitting symplectic resolutions.
Description
C2 C2 ∼= C4.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00209-012-1028-6
