TRIVIALITY OF CERTAIN EQUIVARIANT VECTOR- BUNDLES FOR FINITE CYCLIC GROUPS

We show that if G is a finite cyclic group and V is a complex G-module consisting of the direct sum of a 1-dimensional non-trivial represent ation and a module with trivial action, then all algebraic G-vector bu ndles with base V are trivial. As a consequence, the action of G on th e total space of such a bundle is linearizable. This shows, for exampl e, that certain involutions (actions of Z/2 Z) on C4, which until now were not known to be linearizable, are in fact linearizable. The proof is not constructive, in that it does not give an algorithm to lineari ze such an action.