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arXiv · 2205.00607

Finite abelian subgroups in the groups of birational and bimeromorphic selfmaps

Aleksei Golota
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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 K\"ahler spaces, under some additional assumptions.

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Aleksei Golota. 2022-05-02. Finite abelian subgroups in the groups of birational and bimeromorphic selfmaps. https://arxiv.org/abs/2205.00607

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