We classify simple groups that act by birational transformations on compact complex K\"ahler surfaces. Moreover, we show that every finitely generated simple group that acts non-trivially by birational transformations on a projective surface over an arbitrary field is finite.
The Structure of Algebraic Families of Birational Transformations
Algebraic structures of groups of birational transformations
On Birational Transformations of Pairs in the Complex Plane
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