Projective Generation of Curves (III)

LetA be an affine domain of dimensionn over a field of characteristic zero. Let I A(T) be a local complete intersection ideal of height n such that (I=I 2 ) = 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;!I) of the Euler class groupE(A(T)) obtained as the Euler class of a projectiveA(T)- module. It is proved that such a phenomenon occurs if and only if the naturally induced element (I(0);!I(0)) of the Euler class group E(A) is obtained as the Euler class of a projectiveA-module.