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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive

Izv. RAN. Ser. Mat., 2024 Volume 88, Issue 5, Pages 47–66 (Mi im9568)

Finite abelian subgroups in the groups of birational and bimeromorphic selfmaps

A. S. Golota

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: 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: birational map, bimeromorphic map, compact Kähler space, finite abelian group.

UDC: 512.76+512.78

MSC: 14E05, 14E07, 32J27

Received: 18.12.2023
Revised: 29.03.2024

DOI: 10.4213/im9568


 English version:
Izvestiya: Mathematics, 2024, 88:5, 856–872

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© Steklov Math. Inst. of RAS, 2024