LIFTING OF THE ADDITIVE GROUP SCHEME ACTIONS

Abstract. Let B be a normal affine C-domain and let A be a C-subalgebra of B such that B is a finite A-module. Let δ be a locally nilpotent derivation on A. Then δ lifts uniquely to the quotient field L of B, which we denote by Δ. We consider when Δ is a locally nilpotent derivation of B. This is a classical subject treated in [17, 19, 16]. We are interested in the case where A is the G-invariant subring of B when a finite group G acts on B. As a related topic, we treat in the last section the finite coverings of log affine pseudo-planes in terms of the liftings of the A1-fibrations associated with locally nilpotent derivations. 1