Realisation of linear algebraic groups as automorphism groups

Abstract

Let $G$ be a linear algebraic group, over a field $F$. We show that $G$ is isomorphic to the automorphism group scheme of a smooth projective $F$-variety, defined as the blow-up of a projective space, along a suitable smooth subvariety.

Updated the introduction. 5^2 pages. Comments are welcome:)