Connected algebraic groups acting on 3dimensional Mori fibrations
Abstract
We study the connected algebraic groups acting on Mori fibrations $X \to Y$ with $X$ a rational threefold and $\mathrm{dim}(Y) \geq 1$. 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 $\mathrm{Bir}(\mathbb{P}^3)$, recovering most of the classification results of Hiroshi Umemura in the complex case.
 Publication:

arXiv eprints
 Pub Date:
 December 2019
 arXiv:
 arXiv:1912.11364
 Bibcode:
 2019arXiv191211364B
 Keywords:

 Mathematics  Algebraic Geometry;
 14E07 14E30 14L30 14M20
 EPrint:
 83 pages, comments are welcome