2020/01/01 by Gwyn Bellamy, Johannes Schmitt, Bellamy, Gwyn +3
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2010.00880
Over the past two decades, there has been much progress on the classification\nof symplectic linear quotient singularities V/G admitting a symplectic\n(equivalently, crepant) resolution of singularities. The classification is\nalmost complete but there is an infinite series of groups in dimension 4 - the\nsymplectically primitive but complex imprimitive groups - and 10 exceptional\ngroups up to dimension 10, for which it is still open. In this paper, we treat\nthe remaining infinite series and prove that for all but possibly 39 cases\nthere is no symplectic resolution. We thereby reduce the classification problem\nto finitely many open cases. We furthermore prove non-existence of a symplectic\nresolution for one exceptional group, leaving 39+9=48 open cases in total. We\ndo not expect any of the remaining cases to admit a symplectic resolution.\n