Projective generation of ideals in polynomial extensions

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∕I2 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.