Projective Generation of Curves (III)

Let A be an affine domain of dimension n over a field of characteristic zero. Let I⊂A[T] be a local complete intersection ideal of height n such that μ(I/I²)=n. This paper examines under what condition I is surjective image of a projective A[T]-module of rank n. More specifically, one is interested in knowing when is an element (I,ωI) of the Euler class group E(A[T]) obtained as the Euler class of a projective A[T]-module. It is proved that such a phenomenon occurs if and only if the naturally induced element (I(0),ωI(0)) of the Euler class group E(A) is obtained as the Euler class of a projective A-module.