SMRI Algebra and Geometry Online: Thiel -- Towards the classification of symplectic linear quotient singularities admitting a symplectic resolution

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SMRI Algebra and Geometry Online

'Towards the classification of symplectic linear quotient singularities admitting a 
symplectic resolution'
Ulrich Thiel (University of Kaiserslautern)
Online via Zoom - Register here: https://bit.ly/364HXRI
Thursday 8th July 3:30pm - 5:00pm 

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. Recently, we have proven that for all but possibly 39 cases in the 
remaining infinite series there is no symplectic resolution. We have thereby reduced 
the classification problem to finitely many open cases. We do not expect any of the 
remaining cases to admit a symplectic resolution. This is joint work with Gwyn Bellamy 
and Johannes Schmitt.