A new linear quotient of C^4 admitting a symplectic resolution

Bellamy, G. and Schedler, T. (2013) A new linear quotient of C^4 admitting a symplectic resolution. Mathematische Zeitschrift, 273(3-4), pp. 753-769. (doi: 10.1007/s00209-012-1028-6)

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We show that the quotient C^4/G admits a symplectic resolution for G = (Q_8 x D_8)/(Z/2) < Sp(4,C). 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 -1 of each. It is equipped with the tensor product of the defining two-dimensional representations of Q_8 and D_8. This group is also naturally a subgroup of the wreath product group of Q_8 by S_2. 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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Bellamy, Professor Gwyn
Authors: Bellamy, G., and Schedler, T.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mathematische Zeitschrift
Publisher:Springer Link
ISSN (Online):1432-1823
Published Online:01 January 2013
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