Towards the classification of symplectic linear quotient singularities admitting a symplectic resolution
Abstract
Over the past two decades, there has been much progress on the classification of symplectic linear quotient singularities V/G admitting a symplectic (equivalently, crepant) resolution of singularities. The classification is almost complete but there is an infinite series of groups in dimension 4  the symplectically primitive but complex imprimitive groups  and 10 exceptional groups up to dimension 10, for which it is still open. In this paper, we treat the remaining infinite series and prove that for all but possibly 39 cases there is no symplectic resolution. We thereby reduce the classification problem to finitely many open cases. We furthermore prove nonexistence of a symplectic resolution for one exceptional group, leaving 39+9=48 open cases in total. We do not expect any of the remaining cases to admit a symplectic resolution.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 arXiv:
 arXiv:2010.00880
 Bibcode:
 2020arXiv201000880B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Representation Theory
 EPrint:
 To appear in Math. Z