$\mathbb{G}_a^3$-structures on del Pezzo fibrations

TL;DR

This paper characterizes when del Pezzo fibrations admit $ ext{G}_a^3$-structures, showing they do so precisely when they are $ ext{P}^2$-bundles over $ ext{P}^1$, thus linking geometric structures to bundle types.

Contribution

It establishes a complete classification of $ ext{G}_a^3$-structures on del Pezzo fibrations, identifying the exact conditions under which these structures exist.

Findings

del Pezzo fibrations admit $ ext{G}_a^3$-structures iff they are $ ext{P}^2$-bundles over $ ext{P}^1$

Provides a classification linking algebraic group actions to geometric bundle structures

Enhances understanding of automorphism groups of del Pezzo fibrations

Abstract

In this paper we prove that del Pezzo fibrations admit $\mathbb{G}_{a}^{3}$-structures if and only if they are $\mathbb{P}^2$-bundles over $\mathbb{P}^{1}$.