March 2021, Saitama

**Title:**Families of simple subgroups in the Cremona group arising from del Pezzo fibrations

**Abstract:**

Cremona group of rank nis the group of birational self-maps of the projective space of dimension n. For any subgroup Gof Cremona group there is a rational variety on which Gacts regularly. This allows to translate the study of subgroups of Cremona group into study of G-equivariant geometry of rational varieties. In this talk I will describe some continuous families of rational threefolds with an action of alternating group of rank 5. I will also explain why the corresponding subgroups of the Cremona group are not pair-wise conjugate.