Automorphism groups of Mori Del Pezzo fibrations over an irrational curve

TL;DR

This paper investigates the automorphism groups of Mori Del Pezzo fibrations over irrational curves and classifies maximal connected algebraic subgroups of the birational automorphism group of the product of such a curve with the projective plane.

Contribution

It provides a classification of automorphism groups for Mori Del Pezzo fibrations over positive genus curves and describes maximal connected algebraic subgroups of the birational automorphism group.

Findings

Automorphism groups of Mori Del Pezzo fibrations are characterized over irrational curves.

A classification of maximal connected algebraic subgroups of ir(C imes P^2) is achieved.

Results are valid over any algebraically closed field of characteristic zero.

Abstract

We study the automorphism groups of Mori Del Pezzo fibrations over a smooth projective curve $C$ of positive genus. From that, we obtain a classification of maximal connected algebraic subgroups of $\mathrm{Bir}(C\times \mathbb{P}^2)$. Our results hold over any algebraically closed field of characteristic zero.