Rees algebras of additive group actions

We establish basic properties of a sheaf graded algebras canonically associated to every relative affine scheme $$f:X\rightarrow S$$ endowed with an action the additive group $${\mathbb {G}}_{a,S}$$ over base or algebraic space S, which we call (relative) Rees algebra -action. In case varieties defined field characteristic zero, further {G}}_{a}$$ -action in terms its locally nilpotent derivation. give algebro-geometric characterization pairs consisting variety and on it whose are finitely generated provide algorithm extending van den Essen’s kernel for derivations compute generators these algebras. illustrate several examples played important historical roles development theory applications construction new families threefolds -actions.