Finite 3-Subgroups in the Cremona Group of Rank 3

A note on 3-subgroups in the space Cremona group

“…Proposition 2.10 ([Pr11, 2.4], [Kuz20,4.4]). Assume that X is a threefold with terminal singularities and G is a 3-subgroup in Aut(X) fixing a point x ∈ X.…”

“…For n = 3, the sharp bounds were obtained for p = 2 and p ≥ 5, see Theorem 1.3. For n = 3, p = 3 in the work [Kuz20] the bound r(G) ≤ 4 was obtained modulo 3 exceptional cases. In this work, we prove the following Theorem 1.1.…”

“…Our approach differs from that of [Kuz20]: we do not use the classificational results on threedimensional Gorenstein Fano varieties. This may be useful for possible generalisations.…”

Finite groups of birational transformations

“…Similar technique was also applied to the study of finite p-subgroups and quasi-simple subgroups in Cr 3 (k), see [72,76,83,59,62] and [16].…”