ABSTRACT
This chapter describes the close relation between the concepts of observable action and unipotency: it shows that a group is universally observable (i.e., its action is observable in any variety where it acts rationally) if and only if it is unipotent. It presents a "birational" characterization of the notion of observable action. This characterization is given in terms of the structure of the field of invariant rational functions and of the non emptiness of the interior of the set of closed orbits of maximal dimension. The chapter emphasizes the algebraic aspects of the definition of observable action considering the set up of an affine group acting rationally on a general commutative algebra. It talks about the observable actions of reductive groups and prove in this situation stronger results than in the case of general groups.
