1. Connected algebraic groups acting on Fano fibrations over P¹.
- Author
-
Blanc, Jérémy and Floris, Enrica
- Subjects
AUTOMORPHISM groups - Abstract
Let X/P¹ be a Mori fiber space with general fiber of Picard rank at least two. We prove that there is a proper closed subset S (X, invariant by the connected component of the identity Aut?(X) of the automorphism group of X, which is moreover the orbit of a section s and whose intersection with a fiber is an orbit of the subgroup of Aut?(X) acting trivially on P¹. Such result is a tool to describe equivariant birational maps from X/P¹ to other Mori fiber spaces and therefore finds its applications in the study of connected algebraic subgroups of Bir(X). This represents a first reduction step towards a possible classification of maximal connected algebraic subgroups of the Cremona group of rank 4. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF