Structure of A*-fibrations over one-dimensional seminormal semilocal domains

In this paper we give a structure theorem for an A*-fibration over a one-di mensional noetherian seminormal semilocal domain and show that, in this sit uation, any A*-fibration whose spectrum occurs as an affine open subscheme of the spectrum of an A(1)-fibration (equivalently, an affine line A(1)) is actually A*. The structure theorem provides examples of A*-fibrations over one-dimensional noetherian seminormal semilocal domains whose spectra are not affine open subschemes of any affine line A(1) over the base ring. We a lso construct examples of nontrivial A*-fibrations over one-dimensional noe therian non-seminormal local domains whose spectra are open subschemes of A (1)-fibrations over the base ring. (C) 1999 Academic Press.