A question of Nori: projective generation of ideals

Abstract

Let A be a smooth affine domain of dimension d over an infinite perfect field k and let n be an integer such that 2n ≥ d + 3. Let I ⊂A[T] be an ideal of height n. Assume that I = (f ₁,...,f _n ) + (I ² T). Under these assumptions, it is proved in this paper that I = (g ₁,...,g _n ) with f _i - g _i⊂ (I ² T), thus settling a question of Nori affirmatively.