A variant of noether normalisation

Abstract

Let X be an affine variety over an infinite field k, together with a collection of finite morphisms ƒ_i : X → A^n_i. We prove that for the general 'product' linear projection π_i P_i : π_i A^n_i the composite → π_i A ^s_i, the composite p_o (π_iƒ_i) : X → A∑_is_i is finite, provided ∑_i s_i ≥ dimX. This generalizes the Noether Normalisation theorem, in a manner analogous to Nori'a generalisation of the 'Whitney embedding theorem' for smooth affine varieties. It also extends Nori's theorem (and its generalisation to non-smooth varieties) to more than 2 factors.