Finite abelian subgroups in the groups of birational and bimeromorphic selfmaps

2022/05/02 by Golota, Aleksei · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2205.00607

Abstract

Let X be a complex projective variety. Suppose that the group of birational automorphisms of X contains finite subgroups isomorphic to (ℤ/Nℤ)^r for r fixed and N arbitrarily large. We show that r does not exceed 2dim(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.

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• Finite abelian group actions on weakly Lefschetz cohomologically symplectic manifolds

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