Algebraic subgroups of the plane Cremona group over a perfect field

Abstract

We show that any infinite algebraic subgroup of the plane Cremona group over a perfect field is contained in a maximal algebraic subgroup of the plane Cremona group. We classify the maximal groups, and their subgroups of rational points, up to conjugacy by a birational map.

arXiv commentWith a Corrigendum closing a gap in the classification

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Cited by in corpus (4)

• Generating the plane Cremona groups by involutions
• Tits-type alternative for certain groups acting on algebraic surfaces
• Del Pezzo surfaces of degree $5$ over perfect fields
• On $G$-birational rigidity of del Pezzo surfaces