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Automorphisms of P1-bundles over rational surfaces
In this paper we provide the complete classification of $\mathbb{P}^1$-bundles over smooth projective rational surfaces whose neutral component of the automorphism group is maximal. Our results hold over any algebraically closed field of characteristic zero.
Connected Algebraic Groups Acting on three-dimensional Mori Fibrations
We study the connected algebraic groups acting on Mori fibrations $X \to Y$ with $X$ a rational threefold and $\textrm{dim}(Y) \geq 1$. More precisely, for these fibre spaces, we consider the neutral component of their automorphism groups and study their equivariant birational geometry. This is done using, inter alia, minimal model program and Sarkisov program and allows us to determine the maximal connected algebraic subgroups of $\textrm{Bir}(\mathbb{P}^3)$, recovering most of the classification results of Hiroshi Umemura in the complex case.