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 geometry of singular cubic threefolds
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abstract
We study linearizability of actions of finite groups on singular cubic threefolds, using cohomological tools, intermediate Jacobians, Burnside invariants, and the equivariant Minimal Model Program.
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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.