Finite abelian subgroups in the groups of birational and bimeromorphic selfmaps

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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.

About the authors

Alexey Sergeevich Golota

Steklov Mathematical Institute of Russian Academy of Sciences

ORCID iD: 0000-0002-5632-3963
Scopus Author ID: 57219245520
ResearcherId: M-1425-2017
without scientific degree

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