Geodesic
Finite abelian subgroups in the groups of birational and bimeromorphic selfmaps
Izvestiya. Mathematics , Tome 88 (2024) no. 5, pp. 856-872

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Let $X$ be a complex projective variety. Suppose that the group of birational automorphisms of $X$ contains finite subgroups isomorphic to $(\mathbb{Z}/N\mathbb{Z})^r$ for $r$ fixed and $N$ arbitrarily large. We show that $r$ does not exceed $2\dim(X)$. Moreover, the equality holds if and only if $X$ is birational to an abelian variety. We also show that an analogous result holds for groups of bimeromorphic automorphisms of compact Kähler spaces under some additional assumptions.
Keywords: compact Kähler space, finite abelian group.
Mots-clés : birational map, bimeromorphic map 
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     author = {A. S. Golota},
     title = {Finite abelian subgroups in the groups of birational and bimeromorphic selfmaps},
     journal = {Izvestiya. Mathematics },
     pages = {856--872},
     publisher = {mathdoc},
     volume = {88},
     number = {5},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2024_88_5_a1/}
}
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A. S. Golota. Finite abelian subgroups in the groups of birational and bimeromorphic selfmaps. Izvestiya. Mathematics , Tome 88 (2024) no. 5, pp. 856-872. http://geodesic.mathdoc.fr/item/IM2_2024_88_5_a1/