Elements generating a proper normal subgroup of the Cremona group

Serge Cantat (1) , Vincent Guirardel (1) , Anne Lonjou (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Unibas - University of Basel

Consider an algebraically closed field k and the Cremona group of all birational transformations of the projective plane over k. We characterize infinite order elements of this group having a non-zero power generating a proper normal subgroup of the Cremona group.

Domains: Mathematics [math]; Group Theory [math.GR]

Serge Cantat, Vincent Guirardel, Anne Lonjou. Elements generating a proper normal subgroup of the Cremona group. International Mathematics Research Notices, 2021, 10 (10), pp.7339-7371. ⟨10.1093/imrn/rnaa026⟩. ⟨insu-02183141⟩