Finite abelian subgroups in the groups of birational and bimeromorphic selfmaps

A. S. Golota

Izvestiya. Mathematics , Tome 88 (2024) no. 5, pp. 856-872.

Résumé

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.

Détail

Keywords: compact Kähler space, finite abelian group.
Mots-clés : birational map, bimeromorphic map

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