Umemura quadric fibrations and maximal subgroups of ${\mathrm{Cr}}_n(\mathbb{C})$

Abstract

We study the equivariant geometry of special quadric fibrations, called Umemura quadric fibrations, as well as the maximality of their automorphism groups inside ${\mathrm{Cr}}_n(\mathbb{C})$. We produce infinite families of pairwise non-conjugate maximal connected algebraic subgroups of ${\mathrm{Cr}}_n(\mathbb{C})$.