Maximal algebraic subgroups of the Cremona group of three variables—Imprimitive algebraic subgroups of exceptional type

Abstract

Enriques and Fano [4], [5] classified all the maximal connected algebraic subgroups of Cr3. Our aim is to give modern and rigorous proofs to their results. In [10], we studied the primitive subgroups. In this paper, we deal with exceptional imprimitive groups. The imprimitivity is an analytic notion. The natural translation of the imprimitivity in algebraic geometry is the de Jonquières type operation (definition (2.1)). Every de Jonquières type operation is imprimitive. However, the difference of these notions is subtle.