Projective generation of ideals in polynomial extensions

Abstract

Let R be an affine domain of dimension n ≥ 3 over a field of characteristic 0. Let L be a projective R[T ]-module of rank 1 and I ⊂ R[T ] a local complete intersection ideal of height n. Assume that I/I is a surjective image of L⊕R[T ]n−1. This paper examines under what conditions I is a surjective image of a projective R[T ]-module P of rank n with determinant L.