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Finite abelian subgroups of the Cremona group of the plane. (English) Zbl 1111.14003

The Cremona group \(\text{Cr}(\mathbb{P}^2)\) of the plane is the group of birational maps of \(\mathbb{P}^2(\mathbb{C})\) into itself. The author presents the classification of finite cyclic subgroups of \(\text{Cr}(\mathbb{P}^2)\). He also gives some results that follow from this classification.

MSC:

14E07 Birational automorphisms, Cremona group and generalizations
14E05 Rational and birational maps
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References:

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