A finite subgroup of the plane Cremona group is linearizable if and only if its G-Mori fibre space model is one of a short list of del Pezzo or Hirzebruch surface types, completing the linearization problem.
Equivariant birational geometry of cubic fourfolds and derived categories
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abstract
We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.
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Linearization problem for finite subgroups of the plane Cremona group
A finite subgroup of the plane Cremona group is linearizable if and only if its G-Mori fibre space model is one of a short list of del Pezzo or Hirzebruch surface types, completing the linearization problem.